Physics Topic Practice

The motor must supply more energy than it usefully delivers because it is only 40% efficient, so divide the lifting work (mgh) by the efficiency to get the input energy, then divide by the input power to get the time (45 s).

Break the motion into three phases and add the distances; the accelerating and decelerating phases cover only half of (max speed x time) because the speed is changing, so each is a triangle on a speed-time graph while the middle phase is a rectangle.

Force on a Current-Carrying Wire in a Magnetic Field

Why the correct answer is right: The magnetic force on a wire follows the equation: F = BIL

• B = magnetic field strength (Tesla)
• I = current in the wire (Amperes)
• L = length of wire in the field (meters)

These three factors directly multiply together to give the force magnitude.

Key concept: When electric current flows through a wire in a magnetic field, the moving charges experience a force that transfers to the wire itself.

Helpful tips:

• Remember "BIL" as your formula
• All three factors must be present - no current means no force, no magnetic field means no force, no wire length means no force
• The force is maximized when the wire is perpendicular to the magnetic field
• This principle is used in electric motors and loudspeakers

Note: The angle between wire and field affects force direction but these three factors determine the magnitude.

Why 45 N is correct: For a balanced beam the clockwise and anticlockwise moments about the pivot must be equal (the principle of moments: force × perpendicular distance). The 60 N force acts 1.5 m from the pivot, giving a moment of 60 × 1.5 = 90 N·m. The balancing force F acts at the far end, which is half of the 4.0 m beam = 2.0 m from the pivot, so F × 2.0 = 90, giving F = 45 N.

Common mistakes: Answering 60 N comes from assuming the two forces must be equal and forgetting that they act at different distances. Getting 80 N comes from inverting the distance ratio (multiplying 60 by 2.0/1.5 instead of balancing the moments). Getting 180 N comes from using the full 4.0 m length, or multiplying the 90 N·m moment by 2.0 m instead of dividing by it.

First use the series resistance (4.0 + 2.0 = 6.0 ohm) and Ohm's law to find I = 2.0 A, then apply F = BIL for one wire and multiply by the 3 turns to get 0.60 N. Skipping the series resistor or the number of turns each lands you on a wrong but plausible value.

Why D is Correct: Magnetic field lines always flow from the north pole to the south pole in smooth, curved paths. The lines are denser (closer together) near the poles because the magnetic field is strongest there. Iron filings naturally align with these invisible field lines, revealing this characteristic pattern.

Why Other Options are Wrong:

• Straight lines: Magnetic fields curve around the magnet, never forming straight lines except directly along the magnet's axis
• Lines going from south to north: This violates the fundamental rule of magnetic field direction
• Evenly spaced lines: Field strength varies, so lines must be closer at poles where the field is strongest

Helpful Tips:

• Remember: "North to South" for field direction
• Closer lines = stronger field (like near the poles)
• Iron filings act like tiny compass needles, showing field direction
• The pattern looks similar to how hair stands up around a charged balloon

Why C is Correct ✓

The direction of rotation remains the same because the motor's torque depends on the interaction between TWO factors:

• Magnetic field direction
• Current direction (which determines armature magnetic field)

When you reverse BOTH factors simultaneously, they cancel each other out. It's like multiplying two negative numbers - you get a positive result!

Why Other Options Are Wrong ❌

• "Rotation reverses": This only happens when you change ONE factor, not both
• "Motor stops": The motor still has torque and will continue running
• "Speed changes": Direction changes don't affect the magnitude of torque

Helpful Memory Tip 💡

Remember the "Double Negative Rule":

• Reverse one thing = rotation reverses
• Reverse two things = rotation stays the same

Think of it like steering a car - if you reverse both the steering wheel AND flip the front/back of the car, you'll still turn the same way relative to your destination!

You must first reduce the network (parallel then series) to get the total current, then split the current back into the 6 ohm branch before using P = I^2 R. The full battery voltage is not across the 6 ohm resistor because the 2 ohm series resistor takes a share.

Work column by column: P = X AND Y is 1 in only the two rows where X and Y are both 1, and in both of those Q is also 1, so the final NAND outputs 0 there and outputs 1 everywhere else, giving 6 ones.

Each spring's stiffness is k = 2 N/cm, and because springs in series both feel the full 8 N load, each stretches 4 cm, so the two together stretch 8 cm in total.

For identical resistors in parallel, divide one resistance by the number of resistors: 4Ω ÷ 3 = 1.33Ω. The total is always smaller than any single resistor.

The AND gate symbol is a D-shape: a flat straight back for the two inputs and a smooth curved front for the output. Because there is no bubble (NAND) and there are two inputs (not NOT), it must be an AND gate.

Why this is correct: With identical batteries (same voltage V) and identical resistors (each R), use I = V/R for each circuit. Two resistors in series double the total resistance to 2R, giving the smallest current (V/2R); the single resistor has resistance R, giving a medium current (V/R); two resistors in parallel halve the total resistance to R/2, giving the largest current (2V/R). So the ranking is series smallest, single in the middle, parallel largest — the choice with the single resistor at medium, the series pair smallest, and the parallel pair largest.

Common mistakes: Many students mix up series and parallel and claim the series circuit has the largest current — but adding a resistor in series adds resistance and reduces current. Others forget that parallel resistors give less total resistance (R/2), and therefore more current, not less. Remember: more paths for the current means lower resistance and higher current.

The cable's resistance drops the current below the rated value, so the heater runs at 500 W, not its marked 720 W; over 100 s it transfers 50 kJ. You must find the heater's resistance, the series current, then its actual power before working out the energy.

Why the correct answer is right:

When a liquid is heated at constant volume, the container size stays fixed. Since liquids have particles that are already close together and relatively incompressible, the average distance between particles remains approximately the same. The added heat energy increases particle movement (kinetic energy) but doesn't significantly change spacing.

Why other answers are wrong:

• "Distance increases" would be correct if volume could expand, but we're told volume is constant
• "Distance decreases" would require compression, which isn't happening here

Helpful tips:

• Key phrase: "constant volume" = container size is fixed
• Remember: liquids are nearly incompressible (particles already tightly packed)
• Heat at constant volume → more particle vibration, not more spacing
• Think of heating soup in a sealed, rigid container - particles move faster but stay roughly the same distance apart

The constraint of constant volume is crucial to this answer!

Why Steel is Correct: Sound travels fastest through steel because it's the densest, most rigid material. Sound waves move by transferring energy between particles - the closer and more tightly bound the particles are, the faster energy transfers. Steel's molecules are packed extremely tight with strong bonds, creating an efficient "highway" for sound waves.

Why Others are Wrong:

• Air: Gas particles are spread far apart with weak connections, making sound transfer slow (~343 m/s)
• Water: Liquid particles are closer than air but still less organized than solids (~1500 m/s)
• Steel: Solid particles are tightly packed and organized (~5000+ m/s)

Helpful Tips:

• Remember: Solids > Liquids > Gases for sound speed
• Think of it like a chain reaction - tighter connections = faster reactions
• Exception: Temperature affects speed too (warmer = faster in same medium)

Why D is Correct: Specific heat capacity tells us how much energy is needed to raise 1 gram of a substance by 1°C. When equal masses receive equal energy, the substance with the highest specific heat capacity will have the smallest temperature rise because it "absorbs" more energy per degree of temperature change.

Think of it like a sponge - substances with high specific heat capacity are like big sponges that soak up lots of energy without getting much hotter.

Why Others Are Wrong:

• Lowest specific heat capacity → largest temperature rise (not smallest)
• Density and molecular structure don't directly determine temperature change from heating

Helpful Tips:

• Remember: Q = mcΔT (energy = mass × specific heat × temperature change)
• Water has high specific heat capacity - that's why oceans moderate Earth's temperature
• Metals typically have low specific heat capacity - they heat up quickly

Why this is correct: This is the displacement method. Note the water level before adding the object, fully submerge the object, then read the new (higher) level. The rise in level — found by subtracting the initial reading from the final reading — equals the volume of water pushed aside, which is exactly the volume of the solid.

Common mistakes: Adding the two readings instead of subtracting them gives a number about twice too big and has no physical meaning. Trying to catch the overflowing water needs a displacement (eureka) can, not an ordinary measuring cylinder filled to the brim. Measuring the dimensions with a ruler and multiplying only works for regular shapes like cubes, so it fails for an irregular object.

Heat Conduction in Metals 🔥

Why D is correct: When a metal rod is heated, thermal energy makes particles vibrate faster and with greater amplitude. However, in solids, particles are held in fixed positions by strong bonds - they can't move freely like in liquids or gases. The vigorous vibrations transfer energy to neighboring particles, conducting heat along the rod.

Why other answers are wrong:

• If particles moved freely, the metal would melt/become liquid
• If particles stopped vibrating, the rod would cool down instead
• If particles broke bonds completely, the metal structure would collapse

Helpful tips:

• Remember: Solids = fixed positions, vibrating particles
• Think of particles as balls connected by springs - they shake but stay in place
• Heat = increased particle movement (vibration)
• Metals conduct heat well because their particles are closely packed and transfer vibrations efficiently

Key concept: Thermal conduction = energy transfer through vibrations, not particle movement!

When waves diffract through a gap they spread out, but their speed and frequency do not change, so the wavelength stays exactly the same. Only the pattern of the wave spreads, not the wavelength itself.

The bobbing gives the period (4 s), so the frequency is 0.25 Hz; the crest spacing is the wavelength (8 m), so v = f x lambda = 2 m/s, and travelling 80 m at 2 m/s takes 40 s.

Why A is Correct: v = fλ is the fundamental wave equation where:

• v = wave speed (what we're finding)
• f = frequency (50 Hz - given)
• λ = wavelength (6.8 m - given)

This equation directly relates the three key wave properties and is perfect when you have frequency and wavelength.

Why Other Options Are Wrong:

• v = f/λ - This would give units of Hz/m = s⁻²m⁻¹, which isn't speed
• v = λ/f - This gives units of m/Hz = m·s, also not speed (m/s)
• v = f + λ - Adding different units (Hz + m) is meaningless

Helpful Tips:

• Remember: Wave speed = frequency × wavelength
• Check units: (Hz)(m) = (s⁻¹)(m) = m/s ✓
• Think logically: Higher frequency OR longer wavelength = faster wave
• This equation works for ALL types of waves (sound, light, water, etc.)

Get the current from P = VI, then use the in-field length 0.40 m (2 turns x 0.20 m) in F = BIL to get 0.60 N, and finally divide by g to convert that lifting force into a mass of 60 g.

Double the cliff distance to get v_air = 340 m/s, use v = flambda to get the source frequency 850 Hz, then apply v = flambda in water (same frequency, faster speed) to get 1360/850 = 1.6 m.

Gravitational Field Strength Unit: N/kg

Why N/kg is correct: Gravitational field strength measures the gravitational force per unit mass at a point. Since:

• Force is measured in Newtons (N)
• Mass is measured in kilograms (kg)
• Field strength = Force ÷ Mass

The unit is N/kg (Newtons per kilogram).

Why other options are wrong:

• N·kg: This would be force × mass, not force ÷ mass
• kg/N: This is the inverse relationship (mass per force)
• m/s²: While gravitational field strength numerically equals acceleration due to gravity, the question asks for field strength units specifically

Helpful tip: Remember that "per" means division! Gravitational field strength tells you how many Newtons of force act on each kilogram of mass. On Earth, g = 9.8 N/kg, meaning every kilogram experiences 9.8 N of gravitational force.

Why C is Correct: To determine if a wave is regular, you need to verify it has consistent periodicity. This means measuring the distance between identical points on consecutive waves (like peak to peak or trough to trough) across the entire screen. If these spacings are identical, the wave has a constant period and is therefore regular.

Why Other Options Are Wrong:

• Checking only amplitude (wave height) isn't enough - waves can have consistent amplitude but irregular timing
• Looking at just one cycle doesn't show the pattern's consistency
• Measuring frequency at one point doesn't reveal variations across time

Helpful Tips:

• Use the oscilloscope's grid lines to measure distances accurately
• Pick the same reference point on each wave (like peaks)
• Check at least 3-4 consecutive cycles
• A regular wave will have evenly spaced, repeating patterns

Remember: Regularity = consistent spacing between cycles!

Why D is Correct: When parallel rays of light pass through a converging lens, they meet at the focal point. The distance from the lens center to this focal point is the focal length. Since the rays meet 15 cm from the lens center, and the diagram shows focal length = 15 cm, this confirms the measurement is accurate.

Why Other Options Are Wrong:

• Any answer suggesting the measurement is incorrect ignores the fundamental definition of focal length
• The focal point location directly determines focal length - there's no error here

Helpful Tips:

• Remember: Focal length = distance from lens center to focal point
• Key rule: Parallel rays always converge at the focal point in converging lenses
• Visual check: If parallel rays meet at the marked focal point, your focal length is correct
• This is how focal length is actually measured in practice!

Bottom line: The diagram shows a perfectly correct focal length measurement.

Why C is Correct: When a sound source moves toward you, the waves get "bunched up" or compressed. The source is essentially chasing its own waves, making them closer together. This creates shorter wavelengths that reach your ears.

Why Other Options Are Wrong:

• "Wavelength increases" - This would happen if the source moved AWAY from you
• "Wavelength stays the same" - This ignores the relative motion between source and observer
• "No sound is detected" - Motion doesn't eliminate sound, just changes its properties

Helpful Tips:

• Memory trick: Moving toward = waves compressed = shorter wavelength
• Think of a siren approaching: the pitch sounds higher because shorter wavelengths = higher frequency
• This is the Doppler Effect - crucial for understanding radar, astronomy, and medical ultrasounds
• Remember: toward = compressed/shorter, away = stretched/longer

Build the force in stages: get the oil's volume, turn it into mass with density, add the tank's mass, convert the whole thing to a weight with g, then divide that weight by the base area to get the pressure (4300 Pa). Skipping the tank's mass, using water's density, or mis-reading a dimension each lands you on a wrong but tempting answer.

Track A and Z separately through the chain: alpha emission gives A-4, Z-2 while beta-minus gives A unchanged, Z+1; then neutrons = final A minus final Z = 220 - 85 = 135.

What Happens When Liquid Boils:

Why B is Correct: At the boiling point, liquid molecules have enough energy to escape as gas throughout the entire liquid, not just at the surface. This creates bubbles of vapor that rise to the surface, causing the rapid, vigorous bubbling we see when water boils.

Why Other Answers Are Wrong:

• If it said "only at the surface" → That's regular evaporation, not boiling
• If it said "molecules slow down" → Wrong! They actually speed up and gain energy
• If it said "temperature keeps rising" → Wrong! Temperature stays constant during boiling

Helpful Tips:

• Evaporation = slow, surface-only (like puddles drying)
• Boiling = fast, throughout entire liquid (bubbles everywhere)
• At boiling point, added heat goes into changing state, not raising temperature
• Think: bubbles = boiling, no bubbles = just evaporation

Average speed uses total path length (700 m) while average velocity uses the straight-line displacement (500 m from Pythagoras); dividing each by the 200 s total gives 3.5 m/s and 2.5 m/s, a difference of 1.0 m/s.

Where Are Electrons and What's Their Charge?

Correct Answer: Outside the nucleus, negative charge

Why This is Right:

Electrons orbit around the nucleus in electron shells/energy levels, similar to planets orbiting the sun. They carry a negative electrical charge (-1).

Why Other Options Are Wrong:

• Inside the nucleus: Only protons (+) and neutrons (neutral) are in the nucleus
• Positive charge: Electrons are always negative; protons are positive
• No charge: Electrons definitely have charge (negative)

Memory Tips:

• "Electrons are External" - they're outside the nucleus
• "Negative Nancy" - electrons are negative (opposite of protons)
• Think of the atom like a solar system: nucleus = sun (center), electrons = planets (orbiting outside)
• Remember: Protons are Positive, Electrons are nEgative (opposite letters in alphabet!)

The negative electrons are attracted to the positive protons, keeping them in orbit around the nucleus.

Work out the input power with P = VI, scale it down by the 80% efficiency to get the useful (heating) power, then use t = E/P with the useful energy and useful power to get 25 s.

When a wave crosses into a new medium its frequency stays the same, but because the speed increases the wavelength increases too (lambda = v/f).

The force on the motor coil increases when the magnetic field is stronger, the current is larger, or there are more turns of wire. Lengthening the connecting wires does none of these, so only changes 1, 2 and 3 help.

Chain kinematics to get the impact speed, then kinetic energy, then keep only the 80% that survives air resistance, and finally use work = force x distance to get the ground's average resisting force: 1600 N.

Why A is Correct: For accurate temperature readings, the liquid must expand uniformly (linearly) with temperature changes. This means equal temperature increases produce equal volume increases. When expansion is uniform, you can mark the thermometer scale evenly, and each degree change moves the liquid the same distance up the tube.

Why Other Options are Wrong:

• If expansion isn't uniform, the scale markings would be uneven and readings inaccurate
• Properties like color or density don't affect measurement accuracy
• Very rapid expansion might make readings hard to see, but uniformity is more critical

Helpful Tips:

• Think "uniform = accurate scale"
• Mercury and alcohol work well because they expand predictably
• Imagine if the liquid expanded a lot for the first 10°C but barely moved for the next 10°C - your thermometer would be useless!
• Linear expansion allows consistent, reliable measurements

The base feels both the air pressing on the oil's surface and the oil's own weight, so add atmospheric pressure to ρgh before multiplying by the base area (remember to square the side length).

Why D is Correct: Induced voltage depends on changing magnetic flux, not just the presence of a magnetic field. When the magnet moves toward the coil, the magnetic field strength through the coil increases, creating a changing flux that induces maximum voltage. When stationary inside the coil, even though the magnetic field is strongest, it's not changing - so induced voltage drops to zero.

Why Other Options Are Wrong:

• "Zero while moving" ignores that moving magnets create changing flux
• "Maximum while stationary" confuses field strength with changing flux
• "Constant throughout" misses that only flux changes matter

Helpful Tips:

• Remember Faraday's Law: Induced voltage = rate of change of magnetic flux
• Key word: "changing" - no change = no induced voltage
• Think of it like speed vs. acceleration - a fast car (strong field) at constant velocity (stationary magnet) has zero acceleration (no induced voltage)

Why the fuse is correct: A fuse contains a thin piece of wire that heats up as current passes through it. If the current rises above the fuse's rated value, this wire gets hot enough to melt, which breaks the circuit and stops the current flowing. This protects both the appliance and the user.

Common mistakes: Picking the earth wire confuses two different jobs. The earth wire is a safety path that carries current to the ground if a fault makes the metal casing live, but it does not switch the current off on its own when the current is too large. Choosing the live or neutral wire is also wrong because those wires simply carry the current around the complete circuit and have no mechanism to break it.

When Water Freezes: Molecular Motion Changes

Why C is Correct: When liquid water freezes at 0°C, two key changes happen:

• Slower movement: Ice molecules vibrate in fixed positions instead of flowing freely like in liquid water
• More ordered arrangement: Molecules form a rigid, organized crystal structure (hexagonal pattern) rather than the random clustering in liquid water

Why Other Answers Are Wrong:

• If molecules moved faster, the substance would become gas, not solid
• If molecules became less ordered, they'd remain liquid or become gas
• Temperature stays 0°C during freezing, so average kinetic energy remains constant

Helpful Tips:

• Remember: Solid = organized structure, limited movement
• Liquid = some organization, more freedom to move
• Gas = chaotic, maximum movement
• During phase changes at constant temperature, molecular arrangement changes but average kinetic energy stays the same

Think of it like students going from recess (liquid) to organized rows in class (solid)!

The frequency stays the same when light enters glass, so the slower speed ($c/n$) forces a shorter wavelength; computing the air and glass wavelengths from the period and refractive index gives a decrease of 200 nm.

First turn the light-year into metres using distance = speed x time, scale it up by the number of light-years to get the galaxy distance in metres, then multiply by the Hubble constant to get the recession speed; keeping every quantity in SI units gives $1.08 \times 10^{7}$ m/s.

Why B is Correct: All objects in free fall have the same acceleration due to gravity (g = 9.8 m/s²), regardless of their mass. This is because gravitational force increases with mass, but so does inertia (resistance to acceleration). These effects cancel out perfectly, giving identical acceleration.

Why Other Options are Wrong:

• Different accelerations: Mass doesn't affect gravitational acceleration
• Heavier falls faster: This is a common misconception - mass doesn't determine fall speed in a vacuum
• Lighter falls faster: Same misconception in reverse

Helpful Tips:

• Think of Galileo's famous experiment at the Leaning Tower of Pisa
• Air resistance is ignored in physics problems unless specifically mentioned
• Remember: F = ma, but gravitational force F also depends on mass, so they cancel out
• All objects fall at the same rate in a vacuum (like on the Moon)

The key insight: gravity affects all objects equally!

Why the Mass Stays the Same

Why B is correct: When you reshape modeling clay, you're only changing its form, not removing or adding any clay material. Mass measures the amount of matter in an object - since no clay is lost or gained during reshaping, the mass remains identical.

Why other answers are wrong:

• "Mass increases" - Wrong! You haven't added any extra clay
• "Mass decreases" - Wrong! No clay was removed or lost
• "Mass doubles" - Wrong! The amount of clay material is unchanged

Helpful Tips:

• Think of mass as "how much stuff" you have
• Only adding or removing material changes mass
• Changing shape ≠ changing mass
• This applies to all materials: playdough, water in different containers, crumpled vs. flat paper

Remember: Mass stays constant when you only change an object's shape or form!

A wave's frequency is fixed by its source, so it does not change when the wave enters a new medium - only the speed and wavelength change. Calculating f in the warm air gives 40 kHz, and that is its value in the cooler air too.

Each ray sits 38° from the normal on opposite sides, so the angle between the incident and reflected rays is 2 × 38° = 76°.

Why this is correct: The pitch of a sound, meaning how high or low it sounds, is set by its frequency (the number of vibrations per second, measured in hertz). A higher frequency gives a higher pitch, and a lower frequency gives a lower pitch.

Common mistakes: The most frequent error is choosing amplitude, which controls loudness (how big the vibration is), not pitch. Picking diffraction or refraction mixes up pitch with general wave behaviours: these describe how waves bend around obstacles or change direction when entering a new medium, and neither affects how high or low a sound seems.

Why D is Correct: The correct answer perfectly matches the fundamental charges of atomic particles:

• Protons carry a positive (+) charge
• Electrons carry a negative (-) charge
• Neutrons are neutral (no charge)

Think of it like this: Proton = Positive, Electron = nEgative, Neutron = Neutral.

Why Other Answers Are Wrong: Any option that mixes up these charges contradicts basic atomic structure. For example, if protons were negative and electrons positive, atoms wouldn't behave as we observe them in nature.

Helpful Tips:

• Remember: Opposite charges attract (protons and electrons), which keeps electrons orbiting the nucleus
• Neutrons have no charge, so they don't affect electrical interactions
• The number of protons determines an element's identity
• In neutral atoms, protons = electrons, so positive and negative charges balance out

Why "watt" is correct:

Electrical power is calculated using the formula: Power = Current × Voltage

When current is in amperes (A) and voltage is in volts (V), the unit becomes:

• A × V = Watt (W)

This is the standard SI unit for electrical power, named after James Watt.

Why other options are wrong:

• Joule: Unit of energy, not power
• Coulomb: Unit of electric charge
• Ohm: Unit of electrical resistance

Helpful tips:

• Remember: P = IV (Power = Current × Voltage)
• Think of everyday examples: light bulbs are rated in watts (60W, 100W)
• Power tells you how fast energy is being used
• 1 watt = 1 joule per second

Memory trick: "Watts measure electrical power" - both start with 'W'!

Work and Distance Relationship

Why D is correct: When pushing at constant speed, the applied force remains the same throughout the motion. Since Work = Force × Distance, and force is constant, work done increases directly with distance moved. This creates a straight line through the origin on a graph - double the distance means double the work.

Why other options are wrong:

• Curved relationships: Work doesn't increase exponentially or level off when force is constant
• Inverse relationships: Work increases with distance, not decreases
• No relationship: Work and distance are definitely connected through the work formula

Helpful tips:

• Remember: Work = Force × Distance
• Constant speed = constant force needed
• Direct proportion creates straight lines through origin
• Think practically: pushing twice as far requires twice as much total work

The key insight is recognizing that constant speed means constant force!

Why A is Correct: Iron nail (X) and steel paper clip (Y) are both ferromagnetic materials. Iron is naturally magnetic, and steel contains iron, so both are strongly attracted to magnets. Copper wire (Z) is non-magnetic - it contains no iron and won't be attracted to magnets.

Why Other Options Are Wrong:

• If an option says all three are attracted: Copper is never magnetic
• If an option says only iron is attracted: Steel (which contains iron) is also magnetic
• If an option says none are attracted: This ignores that iron and steel are definitely magnetic

Helpful Tips: 🧲 Remember "IRON" - Iron, steel (contains iron), nickel, and cobalt are magnetic 🚫 Common non-magnetic metals: Copper, aluminum, gold, silver ✅ Quick test: If it contains iron, it's likely magnetic

Think: "Iron attracts iron-based materials!"

Wave Speed Calculation

Why A (300 m/s) is correct: Use the wave equation: speed = frequency × wavelength

• Speed = 50 Hz × 6.0 m = 300 m/s

Why other answers are wrong:

• Adding (50 + 6 = 56): Wrong operation - waves don't work this way
• Subtracting (50 - 6 = 44): Wrong operation
• Dividing (50 ÷ 6 = 8.3): This would give frequency if you had speed and wavelength

Helpful Tips:

1. Remember the formula: v = fλ (speed = frequency × wavelength)
2. Units check: Hz × m = m/s ✓
3. Memory trick: "Speed equals frequency times lambda"
4. Common mistake: Don't confuse this with v = λ/T (period formula)

The wave travels 300 meters every second!

Finding Universe's Age from Hubble Constant

Why B is correct: The age of the universe ≈ 1/H₀, but we need unit conversion!

H₀ = 70 km s⁻¹ Mpc⁻¹ = 70 km s⁻¹ per 3.26 × 10¹⁹ km

This gives H₀ ≈ 2.2 × 10⁻¹⁸ s⁻¹

Age = 1/H₀ ≈ 4.5 × 10¹⁷ seconds

To convert to years: divide by seconds per year (3.16 × 10⁷)

Therefore: Age = 1/(H₀ × 3.16 × 10⁷) years ✓

Why others are wrong:

• Missing the seconds→years conversion factor
• Using incorrect conversion factors
• Wrong mathematical operations

Helpful tips:

• Remember: 1 year ≈ 3.16 × 10⁷ seconds (≈ π × 10⁷)
• Always check units match your final answer
• The "Hubble time" 1/H₀ gives a rough universe age, but needs proper units

You must strip the constant background off both readings before working out the half-life, then add it back on at the very end because the counter always measures source plus background together. Here that gives a 5 min half-life and a final total of 40 counts/min.

Always strip the background from a count rate before doing any half-life calculation, then add it back at the end, because the counter measures the true decay plus the ever-present background. Here that gives a half-life of 10 min, four half-lives in 40 min, and a final reading of 60 counts/s.

The pollen grains move randomly because countless tiny, fast-moving water molecules (too small to see) keep hitting them unevenly from different directions. This is Brownian motion, evidence that molecules are in constant random motion.

Why this is correct: A switch placed in series with the lamp is the right way to control it. In a series connection there is only one path for the current, so opening the switch breaks that single loop and the lamp goes off; closing it completes the loop and the lamp lights. That on/off control is exactly what a switch is for.

Common mistakes: The trickiest wrong choice is a switch wired in parallel with the lamp. Closing such a switch creates a low-resistance shortcut beside the lamp, so the current bypasses the lamp (turning it off) and a large current can flow that may blow the fuse, the opposite of control. Other errors come from thinking the switch must sit at the positive terminal or in a separate branch, but in a single loop it doesn't matter where the switch goes, as long as it is in series so it can interrupt the one current path.

Both echoes together give the speed of sound ($v=2S/(t_1+t_2)=320\ \text{m/s}$); the wave equation then gives $\lambda = v/f = 4\ \text{m}$, the near echo gives the distance $v t_1/2 = 80\ \text{m}$, and dividing gives $80/4 = 20$ wavelengths.

Why D is Correct: According to Boyle's Law, pressure and volume have an inverse relationship at constant temperature. When volume doubles, pressure is cut in half. Think of it like a balloon - if you squeeze it to half its size, the pressure inside doubles. The opposite happens when volume increases.

Why Other Answers Are Wrong:

• "Pressure doubles" - This would happen if volume was halved, not doubled
• "Pressure stays the same" - This ignores the inverse relationship between P and V
• "Pressure quadruples" - No gas law supports this relationship

Helpful Tips:

• Remember: P₁V₁ = P₂V₂ (Boyle's Law)
• Use the "seesaw" analogy - when one goes up, the other goes down
• Practice with numbers: If P₁ = 4 atm and V₁ = 2 L, then when V₂ = 4 L, P₂ = 2 atm
• Only works at constant temperature!

Why this is correct: All three trace back to the Sun. Wind blows because sunlight heats the atmosphere unevenly, making warm air rise and cooler air rush in. Hydroelectric power depends on the water cycle, where the Sun evaporates water that later falls as rain and collects behind dams. Fossil fuels are the remains of ancient plants and animals that originally captured the Sun's energy through photosynthesis.

A common mistake is picking chemical energy stored in matter: that is only the immediate store in fossil fuels (and not even relevant to wind or water), not the ultimate source the question asks for. Choosing gravitational potential energy describes how stored water releases energy, but it does not explain what lifted the water there in the first place. Picking the Earth's core confuses this with geothermal energy, which is a different source entirely.

Chain density and volume to get mass, then weight ($W=mg$), then divide by the smallest face area to get the maximum pressure. The block standing on its smallest face means the contact area is the product of the two smallest dimensions.

Why Mass is Correct: Mass measures the actual amount of matter (atoms/molecules) in an object. It stays the same everywhere - a 5kg rock has the same mass on Earth, Moon, or in space.

Why Other Options Are Wrong:

• Weight: Measures gravitational force on an object, not matter itself. Changes with location (you weigh less on the Moon!)
• Volume: Measures space occupied, not amount of matter. A balloon and a marble can have same volume but very different amounts of matter
• Density: Compares mass to volume (mass ÷ volume), but isn't a direct measure of matter quantity

Helpful Tips:

• Think "How much stuff is there?" = Mass
• Mass uses grams/kilograms
• Weight uses Newtons (force units)
• Remember: Mass is constant, weight changes with gravity

Mass directly counts the matter particles, making it the true measure of quantity!

In a convection current, the cooler liquid is denser than the warm liquid, so it sinks. The warm, less dense liquid rises to take its place.

When is Induced EMF Maximum in a Rotating Coil?

Why C is Correct: When the coil is parallel to magnetic field lines, the magnetic flux through it is changing at the fastest rate. At this position, the coil cuts through the maximum number of field lines per unit time, producing maximum induced EMF according to Faraday's law.

Why Other Positions Are Wrong:

• Perpendicular position: Flux is at maximum/minimum value but not changing at that instant, so EMF = 0
• At angles: Flux changes at moderate rates, giving moderate EMF values

Helpful Tips:

• Remember: EMF depends on the rate of change of flux, not the flux value itself
• Think of a sine wave: maximum EMF occurs when the graph has the steepest slope (parallel position)
• Visualize the coil "slicing" through field lines most rapidly when parallel

Key Point: Maximum EMF = Maximum rate of flux change

Why this is correct: Use the wave equation v = f λ, rearranged to λ = v / f. Here λ = (3.0 × 10⁸ m/s) ÷ (3.0 × 10⁹ Hz) = 0.1 m, which is 10 cm. A wavelength of about 0.1 m sits in the microwave band of the electromagnetic spectrum, so the wave is a microwave.

Common mistakes: Dividing the wrong way round (f ÷ v) gives a meaningless tiny "wavelength" and leads to picking infrared or ultraviolet. Some students reason "very high frequency must be radio," but radio waves actually have much longer wavelengths (well over a metre). Remember the spectrum order — radio (longest), then microwave, infrared, visible, ultraviolet (much shorter) — and that 0.1 m clearly lands in the microwave region.

Use $P=VI$ to get the input power (1.5 W), divide the total stored energy by that power to find how long it lasts (3600 s), then take 20% of the stored energy for the useful light (1080 J). Efficiency scales the energy, not the time.

Why A is Correct: When a wire is parallel to magnetic field lines, the magnetic force is zero. This happens because the formula for magnetic force is F = BIL sin θ, where θ is the angle between the wire and field. When parallel, θ = 0°, and sin(0°) = 0, making the force zero.

Why Others are Wrong:

• Perpendicular positioning (90°): Creates maximum force since sin(90°) = 1
• Any angled positioning: Produces some force since sin θ > 0 for angles between 0° and 180°

Helpful Tips:

• Remember: Parallel = Zero force, Perpendicular = Maximum force
• Think of it like pushing a door: pushing parallel to the door (along its surface) won't open it, but pushing perpendicular creates maximum effect
• The sine function determines force strength: sin(0°) = 0, sin(90°) = 1

Because the trolleys move in opposite directions, their momenta partly cancel (signs matter), so conservation of momentum gives a combined speed of 4.0 m/s; the kinetic energy of the full 4.0 kg mass at that speed is 32 J.

Average velocity is net displacement divided by total time, so you must find both the full time of flight (2 s up plus 6 s down = 8 s) and the straight-line displacement (160 m to the cliff base), giving 160/8 = 20 m/s; using the 200 m total distance instead would wrongly give the average speed.

Why C is Correct: When temperature increases at constant pressure, gas volume increases proportionally. This follows Charles's Law: V ∝ T (at constant pressure). As molecules heat up, they move faster and need more space, expanding the gas volume.

Key Points:

• Temperature and volume have a direct relationship
• Double the absolute temperature = double the volume
• Must use absolute temperature (Kelvin, not Celsius!)

Common Wrong Answers:

• "Volume decreases" - This would violate Charles's Law
• "Volume stays constant" - This only happens at constant temperature
• "Volume increases exponentially" - The relationship is linear, not exponential

Helpful Tips:

• Remember: Hot air balloons rise because heated air expands and becomes less dense
• Always convert temperature to Kelvin (K = °C + 273)
• Think of molecules as tiny balls bouncing faster when heated - they need more room!

Why C is Correct: During acceleration (0-4s), the car covers increasing distances each second, creating a curved upward line on the distance-time graph. During constant velocity (4-10s), the car covers equal distances each second, creating a straight line with constant positive gradient.

Why Others Are Wrong:

• Straight lines during acceleration would mean constant velocity (no acceleration)
• Horizontal lines would mean the car stopped moving
• Downward curves/negative gradients would mean the car was slowing down or moving backward

Helpful Tips:

• Acceleration = curved line on distance-time graphs
• Constant velocity = straight line with steady gradient
• Stationary = horizontal line
• The steeper the gradient, the faster the speed
• Always check: is distance increasing? (Yes = positive gradient)

Remember: Acceleration means speed is changing, so distance covered per second changes too!

You must build mass from density and volume, convert mass to weight using the planet's own $g$ (not Earth's 10), then divide that weight by the specific face the block actually rests on. Skipping any step, or picking a different face, lands you on one of the wrong options.

Why B is Correct: In a vacuum (no air resistance), ALL objects fall with the same acceleration regardless of their mass. This is 9.8 m/s² downward on Earth. Gravity pulls harder on heavier objects, but heavier objects also resist acceleration more - these effects perfectly cancel out!

Why Other Answers Are Wrong:

• If you picked "heavier accelerates faster" - that's only true WITH air resistance
• If you picked "lighter accelerates faster" - this ignores how gravity actually works
• Different accelerations would mean objects reach the ground at different times, which experiments prove false

Helpful Tips: ✓ Remember: Vacuum = no air resistance = same acceleration for all objects ✓ Think of astronaut David Scott's famous moon experiment: hammer and feather fell together ✓ Mass affects gravitational FORCE, but acceleration stays constant ✓ This is why all objects fall at g = 9.8 m/s² in physics problems

Why D is Correct: In parallel circuits, adding more branches creates additional paths for current to flow. Each new branch reduces the total resistance of the circuit. Since V = IR (Ohm's Law), when voltage stays constant (same battery) but resistance decreases, current must increase.

Why Other Options Are Wrong:

• If an option says current decreases: Wrong - more paths = more current flow
• If an option says current stays the same: Wrong - total resistance changes, so current changes
• If an option says resistance increases: Wrong - parallel branches always decrease total resistance

Helpful Tips:

• Think of parallel branches like adding more lanes to a highway - more paths = more traffic flow
• Remember: In parallel circuits, total resistance is always less than the smallest individual resistance
• Use the analogy: more open doors in a room = easier for people to flow through

Transformer Explanation

Why D is correct: This is a step-up transformer because the secondary coil (500 turns) has more turns than the primary coil (100 turns).

Using the transformer equation: Vs/Vp = Ns/Np

Where:

• Vs = secondary voltage, Vp = primary voltage (12V)
• Ns = secondary turns (500), Np = primary turns (100)

Calculation: Vs/12 = 500/100 = 5 Therefore: Vs = 12 × 5 = 60V

Key Tips:

• Step-up: Secondary has MORE turns → voltage increases
• Step-down: Secondary has FEWER turns → voltage decreases
• The turns ratio directly equals the voltage ratio
• More turns = higher voltage, fewer turns = lower voltage

Memory trick: Think "turns UP = voltage UP" for step-up transformers!

The secondary voltage is 60V, and since voltage increased from 12V to 60V, this confirms it's a step-up transformer.

Why D is Correct: Wind turbines depend entirely on wind to generate electricity. When wind speed is too low (below ~7 mph), turbines don't operate. When it's too high (above ~55 mph), they shut down for safety. This makes wind power intermittent - it can't produce consistent electricity on demand like coal or nuclear plants.

Why Other Options Are Wrong:

• Wind turbines are actually getting cheaper to build and maintain
• They produce minimal noise (about as loud as a refrigerator)
• They don't pollute the air or water during operation

Helpful Tips:

• Remember: Reliability = Consistency
• Wind energy's biggest challenge is storage - we need batteries or backup power sources
• This is why most areas use wind power alongside other energy sources
• Think of it like solar panels not working at night - same concept with wind!

The variability issue is why engineers are developing better energy storage solutions.

Why 80 m is correct:

When a car accelerates uniformly from rest, we use the kinematic equation: s = (u + v)t ÷ 2

Where:

• s = distance
• u = initial velocity = 0 m/s (starts from rest)
• v = final velocity = 20 m/s
• t = time = 8 s

s = (0 + 20) × 8 ÷ 2 = 160 ÷ 2 = 80 m

Common wrong answers:

• 160 m: Forgot to divide by 2
• 40 m: Used average velocity but wrong time calculation
• 2.5 m: Confused with acceleration value (a = 2.5 m/s²)

Helpful tips:

• Remember the "average velocity" concept: (initial + final) ÷ 2
• Always check units match your answer
• Alternative formula: s = ut + ½at² gives the same result
• Draw a velocity-time graph - the area under the triangle equals distance!

Why B is Correct: Steel has high retentivity (ability to retain magnetism) because it's a "hard" magnetic material. Once magnetized, steel keeps its magnetic domains aligned even after the external magnetizing force is removed, staying permanently magnetized.

Iron has low retentivity because it's a "soft" magnetic material. Its magnetic domains easily realign back to random positions when the magnetizing force stops, losing most of its magnetism.

Why Other Options Are Wrong:

• If it says both remain magnetized: Iron doesn't retain magnetism well
• If it says both lose magnetism: Steel is designed to stay magnetized
• If it says iron remains but steel loses: This is backwards

Helpful Tips:

• "Hard" = Holds magnetism (steel, permanent magnets)
• "Soft" = Loses magnetism (pure iron, electromagnets)
• Think: Steel scissors stay magnetic, iron nails in electromagnets don't

Machine Efficiency Formula

Why B is correct: Efficiency measures how well a machine converts input energy into useful work. The formula efficiency = (useful output energy / input energy) × 100% gives you the percentage of input energy that becomes useful output. Since some energy is always lost (usually as heat), efficiency is always less than 100%.

Why other answers are wrong:

• Flipping the fraction (input/output) would give values greater than 100%, which is impossible
• Using power instead of energy changes the concept entirely
• Missing the ×100% means you get a decimal instead of a percentage

Helpful Tips:

• Think "what you get out" ÷ "what you put in"
• Efficiency is always between 0% and 100%
• No machine is 100% efficient due to energy losses
• Remember to multiply by 100 to convert to percentage

Example: If a motor uses 1000J and produces 800J of useful work, efficiency = (800/1000) × 100% = 80%

Temperature Coefficient of Resistance Explanation

Why the correct answer (4.2 × 10⁻³ °C⁻¹) is right:

Using the formula R = R₀(1 + αΔT):

• R₀ = 12 Ω (initial resistance at 20°C)
• R = 15 Ω (final resistance at 80°C)
• ΔT = 80°C - 20°C = 60°C

Substituting: 15 = 12(1 + α × 60)

• 15/12 = 1 + 60α
• 1.25 = 1 + 60α
• 0.25 = 60α
• α = 0.25/60 = 4.17 × 10⁻³ °C⁻¹ ≈ 4.2 × 10⁻³ °C⁻¹

Common mistakes:

• Using wrong temperature values (forgetting to calculate ΔT)
• Algebraic errors when rearranging the formula
• Unit confusion

Helpful tips:

• Always identify R₀, R, and ΔT clearly
• Remember ΔT = final temperature - initial temperature
• Check units match the given answer format

Why A is Correct: Magnetic field strength is indicated by how closely packed the field lines are. At point P (near the north pole), the field lines are crowded together, showing a strong magnetic field. At point Q (farther away), the field lines are spread apart, indicating a weaker magnetic field.

Why Other Options Are Wrong:

• Field strength is NOT greater at Q - the widely spaced lines show weakness
• Field strength is NOT equal at both points - different line spacing means different strengths
• The relationship is clear from the diagram - not indeterminable

Helpful Tips: ✅ Dense field lines = Strong field ✅ Sparse field lines = Weak field ✅ Magnetic field strength decreases with distance from the magnet ✅ Always look at line spacing, not just proximity to poles

Remember: Field lines are like a crowd - packed together means "strong," spread out means "weak"!

Why C is Correct ✅

The probability of decay for any individual nucleus is constant and never changes. Each nucleus has the same chance of decaying in any given time period, regardless of how long the sample has been decaying or how many other nuclei have already decayed.

Think of it like flipping coins - each coin flip has a 50% chance of heads, no matter how many times you've flipped before!

Why Other Options Are Wrong ❌

• "Probability decreases" - Wrong! Individual nuclei don't "remember" time or get more stable
• "Probability increases" - Wrong! Nuclei don't become more likely to decay over time
• "Probability becomes zero" - Wrong! Nuclei can still decay after one half-life

💡 Key Tips:

• Half-life affects the sample, not individual nuclei
• Radioactive decay is random for each nucleus
• Probability = constant for each nucleus throughout the entire process

What's Left After a Supernova? 🌟💥

Why C is correct: When a massive star explodes in a supernova, its core collapses under extreme gravity. If the core is 1.4-3 times our Sun's mass, it becomes a neutron star - an incredibly dense object where protons and electrons are crushed together. If the core exceeds 3 solar masses, it becomes a black hole where gravity is so strong that nothing can escape.

Why other options are wrong:

• White dwarf: Forms when smaller stars (like our Sun) die peacefully, not from supernovas
• Red giant: This is a phase before a star dies, not what's left after
• New star formation: Supernovas can trigger new star birth in nearby gas clouds, but don't directly create new stars

💡 Memory tip: Think "supernova = super collapse" - only the most extreme objects (neutron stars/black holes) can result from such violent explosions!

Speed of Sound: Air vs Water

Why C is correct: Sound travels 4 times faster in water (~1,500 m/s) than in air (~340 m/s). This happens because water molecules are much closer together than air molecules, allowing sound vibrations to transfer more efficiently from one molecule to the next.

Why other answers are wrong:

• Sound does NOT travel faster in air - air is less dense
• The speeds are NOT equal - there's a huge difference
• Sound does NOT travel at the same speed in all materials

Helpful Tips:

• Remember: Denser materials = faster sound
• Think: Water is ~800x denser than air
• Real example: Put your ear underwater in a pool - you'll hear sounds very clearly because they travel so efficiently
• Memory trick: "Dense = Fast" for sound waves

The closer the molecules, the better they can "pass along" the sound vibration!

Why B is Correct: During boiling at atmospheric pressure, water temperature stays constant at 100°C (212°F). Even though you keep adding heat, the temperature doesn't rise because all that extra energy goes into changing liquid water into steam - this is called the "latent heat of vaporization."

Why Other Answers Are Wrong:

• If temperature kept rising, the water would become superheated steam, not regular boiling
• If temperature dropped, the water would stop boiling
• Temperature fluctuations don't occur during steady boiling

Helpful Tips:

• Think of it like a "energy traffic jam" - heat energy gets "stuck" breaking the bonds between water molecules instead of increasing temperature
• This only applies at constant pressure (like normal atmospheric conditions)
• Once all water becomes steam, then temperature can rise again
• This principle applies to all pure substances during phase changes

Find the cube's true weight from its density and volume, then subtract the upthrust, which equals the weight of the water displaced by only the half-submerged volume. The balance reads 200 - 40 = 160 N.

Sound travels faster in water than in air because water is a denser, stiffer medium. So the speed of sound increases when it goes from air into water.

Why this is correct: Use Snell's law, n = sin(incidence) / sin(refraction). Rearranging gives sin(refraction) = sin30° / 1.5 = 0.5 / 1.5 = 0.333, so the angle of refraction is about 19.5°. This makes sense physically: light entering a denser medium (air into glass) bends towards the normal, so the refraction angle must be smaller than the 30° incidence angle.

Watch out for these mistakes: A value of 60° comes from multiplying by 1.5 instead of dividing (sin(refraction) = 1.5 × sin30°), which wrongly bends the ray away from the normal. A value of 70.5° comes from measuring the ray from the glass surface rather than from the normal, giving the complement of the true angle. Choosing 30° means assuming the ray carries straight on with no bending at all.

Alpha Decay Explained:

Why B is correct: An alpha particle is a helium nucleus containing 2 protons and 2 neutrons. When a nucleus undergoes alpha decay, it literally ejects this alpha particle.

• Mass number (total protons + neutrons) decreases by 4 (losing 2 protons + 2 neutrons)
• Atomic number (number of protons) decreases by 2 (losing 2 protons)

Why other answers are wrong: Any answer suggesting increases is impossible—you can't gain particles by ejecting them. Different numbers (like decreasing by 1 or 3) don't match what an alpha particle actually contains.

Helpful Tips:

• Remember: Alpha = 2 protons + 2 neutrons = helium nucleus
• Use the equation: ²³⁸U → ²³⁴Th + ⁴He (alpha)
• Mass number: 238 → 234 (decreases by 4)
• Atomic number: 92 → 90 (decreases by 2)

Light-Dependent Resistor (LDR) Symbol Explanation

Why D is correct: An LDR symbol combines a standard resistor (zigzag or rectangle) with two diagonal arrows pointing TOWARD it. The arrows represent light hitting the component. When light increases, the LDR's resistance decreases - that's why the arrows point toward it, showing light "attacking" the resistance.

Why other options are wrong:

• Arrows pointing AWAY would suggest the component emits light (like an LED)
• No arrows would just be a regular resistor
• Wrong arrow direction or number indicates a different component

Helpful tips:

• Remember: "Light IN, Resistance DOWN" - arrows point IN
• Think of arrows as light rays hitting the sensor
• LDRs are used in automatic streetlights and camera light meters
• The more light hits it, the better it conducts electricity

The key is those incoming arrows - they're your visual clue!

Pressure is the same everywhere in the liquid, so the forces on the pistons are in the same ratio as their areas, and area grows with the square of the diameter. Halving the diameter quarters the area, so the small piston needs only a quarter of the load's weight, i.e. a 40 kg mass.

Why kg is correct: The kilogram (kg) is the official SI (International System of Units) base unit for mass. It's one of the seven fundamental SI base units that all other units are built from.

Why other options are wrong:

• g (gram): This is a derived unit, not a base unit. While commonly used, it's actually 1/1000 of a kilogram
• lb (pound): This is an imperial unit, not part of the SI system
• N (newton): This measures force, not mass (though they're related through F = ma)

Helpful tips:

• Remember "King Kong" = Kilogram for mass
• Don't confuse mass (kg) with weight (N) - mass stays constant, but weight changes with gravity
• Even though we often use grams in daily life, the kilogram is the official base unit
• SI base units are the building blocks - all other units derive from these seven fundamental ones

Nuclear Fission of Uranium-235

Why A is correct: When uranium-235 splits, it follows the law of conservation of charge - the atomic numbers (protons) of the two smaller nuclei must add up to 92 (uranium's atomic number). However, the mass numbers don't add up to 235 because some mass is converted to energy and neutrons are released during fission.

Why other answers are wrong:

• If mass numbers added to 235, no energy would be released (violates E=mc²)
• If atomic numbers didn't add to 92, electric charge wouldn't be conserved
• Both conservation laws must be satisfied simultaneously

Helpful Tips:

• Atomic number = protons (always conserved in nuclear reactions)
• Mass number = protons + neutrons (can decrease due to mass-energy conversion)
• Remember: Fission releases energy because some mass becomes energy
• Typical fission: U-235 → two nuclei + 2-3 neutrons + energy

Why B is Correct:

Use conservation of momentum: Total momentum before = Total momentum after

Before collision:

• 2 kg ball: (2 kg)(6 m/s) = 12 kg⋅m/s
• 3 kg ball: (3 kg)(0 m/s) = 0 kg⋅m/s
• Total = 12 kg⋅m/s

After collision:

• 2 kg ball: (2 kg)(3 m/s) = 6 kg⋅m/s
• 3 kg ball: (3 kg)(v) = ?
• Total must still = 12 kg⋅m/s

Solving: 6 + 3v = 12 Therefore: v = 2 m/s

Why Others Are Wrong: Other answers would violate momentum conservation - the total momentum wouldn't equal 12 kg⋅m/s.

Helpful Tips:

• Always identify "before" and "after" scenarios
• Remember: momentum = mass × velocity
• Total momentum stays constant in collisions
• Set up the equation: momentum before = momentum after

First convert the electrical supply into input power with $P=VI$, scale it down by the 75% efficiency to get the useful lifting power, then use power = force × speed (or work = weight × height) to reach the time. Each option hides a single classic slip, so only the full four-step chain gives 8 s.

Why this is correct: Use Fleming's left-hand rule for a positive charge (treat its motion as conventional current). Point your First finger (Field) into the page and your seCond finger (Current) to the right; your thuMb (force/Motion) then points upward, so the magnetic force acts upward.

Common mistakes: Choosing "downward" usually means the left and right hands were swapped, or the charge was wrongly treated as negative (a negative charge would feel a downward force). "To the left" comes from confusing the force direction with the direction of motion, and "out of the page" comes from picking the field axis instead of using the rule, which always gives a force perpendicular to both the velocity and the field.

Conservation of Momentum Problem

Why 2.4 m/s is correct: This is a perfectly inelastic collision (objects stick together). Use conservation of momentum:

Initial momentum = Final momentum m₁v₁ + m₂v₂ = (m₁ + m₂)vf

(2.0 kg)(6.0 m/s) + (3.0 kg)(0 m/s) = (2.0 + 3.0 kg)vf 12 kg⋅m/s = (5.0 kg)vf vf = 2.4 m/s

Common wrong answers:

• 6.0 m/s: Ignores the stationary object's mass
• 3.0 m/s: Simple average of masses, not momentum conservation
• 1.2 m/s: Calculation error or wrong formula

Helpful tips:

• Always identify collision type (elastic vs. inelastic)
• Remember stationary objects have zero velocity
• Total momentum before = total momentum after
• Final velocity is always less than initial in inelastic collisions
• Check units: kg⋅m/s for momentum

Why D is Correct: Radiation follows an exponential decay law when passing through materials. As aluminum thickness increases, each additional layer absorbs a constant fraction of remaining radiation, not a fixed amount. This creates the characteristic curved exponential decay pattern where count rate drops rapidly at first, then more gradually.

Why Others Are Wrong:

• Linear decrease: Would mean each layer absorbs the same absolute number of particles - this doesn't happen in reality
• Increases: Aluminum absorbs radiation; it cannot increase the count rate
• Stays constant: Some radiation is always absorbed, so count rate must decrease

Helpful Tips:

• Remember: "Each layer absorbs a percentage, not a fixed number"
• Exponential decay creates a curved graph that never quite reaches zero
• This is the same mathematical pattern as radioactive decay itself
• Thicker materials = fewer particles get through

Why A is Correct: Density tells us how much "stuff" (mass) is packed into a certain amount of space (volume). Since both blocks take up the same amount of space, the only way Block X can have more mass is if its material is "packed tighter." This means Block X is made of a denser material.

Why the others are wrong:

• Options suggesting Block X is larger or has more volume are incorrect because the question states they are the same size.
• Options mentioning gravity are wrong because gravity pulls on both blocks equally; the difference in "heaviness" here is caused by the material itself, not a change in gravity.

Helpful Tip: Think of a sponge and a brick of the exact same size. The brick is much heavier because it is denser, even though it takes up the same amount of space as the sponge!

For a uniform liquid the density is constant, so the pressure at a depth is found directly from $p = \rho g h$. Multiplying $1200 \times 10 \times 0.5$ gives $6000\ \text{Pa}$.

Why B is correct: Diffraction is the scientific term for waves spreading out as they pass through a gap or travel around an edge. Imagine water ripples hitting a narrow opening in a harbor wall; they don’t just travel in a straight line—they fan out on the other side.

Why the others are wrong:

• Refraction occurs when a wave changes speed and direction because it moves from one medium into another (like light passing from air into glass).
• Reflection happens when a wave hits a surface and bounces back, like an echo or a mirror image.

Tips and Pitfalls:

• Tip: Diffraction is most noticeable when the size of the gap is similar to the wave's wavelength.
• Common Pitfall: Students often confuse Diffraction with Refraction. Remember: Diffraction is about Dispersing (spreading) through a gap, while Refraction is about waves bending due to speed changes.

All electromagnetic (EM) waves, including radio waves and this unknown wave, travel at the same constant speed in a vacuum: the speed of light ($c$).

The relationship between speed ($v$), frequency ($f$), and wavelength ($\lambda$) is shown by the formula: $v = f \times \lambda$. Since the speed is constant, frequency and wavelength have an inverse relationship. If the frequency increases, the wavelength must decrease. Therefore, a wave with a higher frequency must have a shorter wavelength.

Why other options are wrong:

• Any option suggesting a different speed is incorrect; all EM waves travel at $3 \times 10^8$ m/s in a vacuum.
• Any option suggesting a longer wavelength is incorrect because frequency and wavelength move in opposite directions.

Tip: Think of a jump rope. Shaking it faster (high frequency) creates more "scrunched up" waves (short wavelength). Speed never changes for EM waves in a vacuum!

At $0\ ^\circ\text{C}$, water is at its freezing point. During any phase change, the temperature remains constant, meaning both ice and liquid exist together until the water is completely frozen. To turn from a liquid to a solid, molecules must lose energy (heat) to their surroundings. This loss of energy causes them to slow down and lock into a fixed, ordered crystal structure.

Why other answers are wrong:

• If only liquid or only ice were mentioned, it wouldn't accurately describe the "freezing process" where both states coexist.
• Gaining energy or becoming "less ordered" describes melting (solid to liquid), which is the opposite of freezing.

Helpful Tip: Remember that during a phase change, energy is used to break or form bonds, so the temperature stays exactly the same until the change is finished!

Why it’s correct: When resistors are connected in parallel (Option A), you create multiple paths for the electricity to flow. Think of it like adding extra lanes to a highway; more lanes make it easier for traffic to move, even if the lanes have obstacles. In a parallel circuit, the total resistance is always lower than the resistance of any single resistor in the arrangement.

Why the others are wrong:

• Series arrangements: When resistors are in a single line, the current must push through all of them one after another. This adds the resistances together, making the total resistance much higher.
• Mixed arrangements: Any combination that includes resistors in series will naturally have a higher resistance than a purely parallel setup.

Top Tip: Adding resistors in series increases resistance (like making an obstacle course longer). Adding them in parallel decreases resistance (like opening more doors to exit a building).

Correct Answer: C

Why it’s correct: Wavelength and amplitude are independent properties of a wave.

• Wavelength is the horizontal distance between two peaks (how "wide" the wave is).
• Amplitude is the maximum vertical displacement from the center line (how "tall" the wave is).

Changing how wide a wave is does not automatically change how tall it is. Therefore, Wave X can be wider than Wave Y while still reaching the same height.

Why other options are incorrect: Most incorrect options suggest that wavelength and amplitude are linked (e.g., "Wave X must have a larger amplitude"). In physics, you can change the horizontal stretch of a wave without affecting its vertical height. Other options might mention frequency, but without knowing the speed of the waves, we cannot determine their frequency.

Helpful Tip: Always check your axes! On a displacement-distance graph:

• Y-axis = Amplitude (Vertical)
• X-axis = Wavelength (Horizontal) Because one is vertical and one is horizontal, they don't depend on each other!

Evaporation removes the most energetic (fastest) molecules from the surface, so the average speed of the molecules left behind drops, which means the temperature of the remaining liquid falls.

To find the correct answer, use the formula: Work = Force × Distance.

Why D is correct: The student applies a force of 50 N over a distance of 0.2 m. Calculation: $50\text{ N} \times 0.2\text{ m} = \mathbf{10\text{ Joules}}$ of work. In this specific question, this represents the highest value of energy transferred to the object.

Why the others are incorrect: In physics, "Work" only happens if the object moves in the direction of the force. Other options are usually wrong because:

• No movement: If a student just holds a heavy box or pushes a stationary wall, the distance is zero, so the Work is zero.
• Perpendicular motion: If a student carries a box horizontally, the lifting force is upward but the motion is sideways. This counts as zero work on the box.

Top Tip: Don't confuse "effort" with "work." You might get tired holding a heavy bag, but if it doesn't move, you aren't doing any physics work!

EXPLANATION:

Ultraviolet (UV) and infrared (IR) are both members of the electromagnetic (EM) spectrum. In a vacuum (empty space), all EM waves travel at the exact same constant speed: the speed of light ($3 \times 10^8$ m/s).

Why other options are wrong: Any choice suggesting that one travels faster than the other is incorrect. While UV has a higher frequency and IR has a longer wavelength, these two properties balance each other out perfectly to maintain the same speed ($v = f\lambda$).

Helpful Tips & Pitfalls:

• Energy vs. Speed: A common mistake is thinking that "more energy" means "more speed." UV radiation has more energy than IR, but it does not move faster.
• The Medium Matters: EM waves only change speed when they leave a vacuum and enter a material like glass, water, or air. In a vacuum, they are all equal!

When white light enters a glass prism, it slows down and bends. This is called refraction. However, different colors travel at different speeds inside the glass.

Why C is correct:

• Violet light has a shorter wavelength and slows down the most, causing it to bend at the sharpest angle.
• Red light has a longer wavelength and stays relatively fast, so it bends the least. This difference in bending is what spreads white light into a rainbow.

Why other options are incorrect: Any statement suggesting red bends more than violet—or that they bend equally—is wrong. In glass, the rule is consistent: shorter wavelengths (violet/blue) always refract more than longer wavelengths (red/orange).

Helpful Tip: Remember the order ROYGBIV. Red is at the top because it is the "laziest" bender. Think: "Red stays Relaxed" (bends least), while "Violet is Violent" (bends the most)!

Charge over the first 2 minutes gives the current (I = Q/t), the current and p.d. give the power (P = VI), and power times the new 5-minute time gives the energy (E = Pt). The charge was measured over 2 min, but the energy is asked for over 5 min, so E = QV alone is wrong.

To find the weight of an object, use the formula: Weight = mass × gravitational field strength ($W = m \times g$).

Why B is correct:

1. Convert the units: In physics, mass must be in kilograms (kg). Since there are 1,000 grams in a kilogram, $500\text{g} \div 1000 = 0.5\text{kg}$.
2. Calculate: Multiply the mass by the gravity: $0.5\text{kg} \times 9.8\text{N/kg} = \mathbf{4.9\text{N}}$.

Why the other answers are wrong: Other options are incorrect because they usually come from common mistakes, such as forgetting to convert grams to kilograms (which would give a result of 4,900 N) or dividing the numbers instead of multiplying them.

Common Pitfall: The biggest trap in weight questions is using mass in grams. Always check your units first! If the mass is in grams, divide by 1,000 to get kg before you do anything else.

When light travels from air into glass, it enters a denser medium and slows down, causing it to bend towards the normal. When it exits from glass back into air, it speeds up and bends away from the normal. This makes A the correct choice.

Why other options are wrong:

• Any option suggesting the ray bends away from the normal upon entry is incorrect because light always slows down (and bends towards the normal) when entering a denser material like glass.
• If the ray didn't bend at all, it would imply that air and glass have the same density.

Helpful Tips:

• Remember FAST: Fast to Slow = Towards normal.
• Remember SFA: Slow to Fast = Away from normal.
• Common Pitfall: Always draw your "normal" line at 90° to the surface first to clearly see the direction of the bend!

EXPLANATION:

The correct answer is D. In an atom, protons and neutrons contain nearly all the mass. A proton is about 1,840 times heavier than an electron. To visualize this, if a proton were a heavy bowling ball, an electron would be like a small marble!

Why other options are incorrect:

• Masses are equal: This is false. While protons and electrons have equal but opposite charges, their masses are vastly different.
• Electron is larger: This is incorrect. Electrons are the lightest subatomic particles; their mass is so small it is often rounded to zero in basic chemistry.

Helpful Tip: A common pitfall is confusing charge with mass.

• Charge: Protons (+1) and Electrons (-1) are equal.
• Mass: Protons are heavy; electrons are light.

Always remember: The nucleus (protons and neutrons) is the "heavy" center of the atom!

To find the mass, we must follow two simple steps:

1. Find gravity ($g$) on the new planet: Use the formula for falling objects: $d = \frac{1}{2}gt^2$. Plugging in the numbers: $200 = \frac{1}{2} \times g \times 10^2$. This simplifies to $200 = 50g$, so $g = 4$ m/s².
2. Calculate mass ($m$): Use $W = mg$. The weight ($W$) is 400 N and $g$ is 4. $400 = m \times 4$. Solving for $m$ gives 100 kg.

Why other answers are wrong:

• 40 kg: This is the mass of the crate on Earth ($400/10$). You cannot use Earth's gravity for a different planet.
• 400 kg: This confuses mass (kg) with weight (N).
• 80 kg: This happens if you forget the "$\frac{1}{2}$" in the distance formula.

Common Pitfall: Don’t go on "autopilot" and use $g = 10$! Always calculate the local gravity first if the problem is set on another planet.

EXPLANATION:

Why it’s correct:
As a galaxy moves away from Earth, the light waves it emits are "stretched" by the expansion of space. Because red light has the longest wavelength in the visible spectrum, this stretching causes the light to shift toward the red end. This is known as redshift.

Why other answers are incorrect:

• Blueshift: This is the opposite. It occurs when an object moves toward us, causing light waves to compress into shorter (bluer) wavelengths.
• Reflection/Refraction: These describe light bouncing off a surface or bending through a material; they do not involve the motion of galaxies.

Helpful Tip:
Remember the "Double R" rule: If an object is Receding (moving away), it is Redshifted.

Common Pitfall:
Redshift doesn't mean the galaxy looks bright red; it just means the light's wavelength is longer than it was when it started!

To find the correct pressure, use the formula: Pressure = Force ÷ Area.

1. Identify Force: The weight of the block is 120 N.
2. Identify Area: For the largest surface, use the two biggest dimensions: 100 cm and 200 cm.
3. Convert to Meters: Always use meters for Pascals (Pa). 100 cm = 1 m and 200 cm = 2 m.
4. Calculate: Area = 1 m × 2 m = 2 m².
5. Final Step: Pressure = 120 N ÷ 2 m² = 60 Pa. (Answer A)

Why other answers are wrong:

• 120 Pa: Result from using the medium surface (50 cm × 200 cm).
• 240 Pa: Result from using the smallest surface (50 cm × 100 cm).
• If you don't convert cm to meters, you will get a tiny decimal that doesn't match the options.

Tip: Convert cm to m before calculating the area to avoid confusion! Remember: 1 Pa = 1 N/m².

Heating makes the whole plate expand outward, so the hole grows larger rather than closing. Liquids expand more than solids for the same volume and temperature rise.

You must first strip the background from both count rates, use the corrected values (640 and 80 Bq) to get the half-life (4 h), then count the halvings from 640 Bq all the way down to 5 Bq (7 of them) and multiply by the half-life, measuring time from the first reading.

EXPLANATION:

Convection is the way heat travels through liquids and gases.

Why B is correct: When air is heated, its molecules move faster and spread out. This causes the air to expand. Because the same amount of air now takes up more space, it becomes less dense (lighter) than the cooler air around it. Just like a cork in water, this lighter air floats upward.

Why other options are wrong:

• Air does not contract (shrink) when heated; it expands.
• Warm air does not sink; it is pushed upward by heavier, cooler air.
• Cooling makes air more dense, not less dense.

Helpful Tip: Think of a hot air balloon. The burner heats the air, making it expand and become less dense than the outside air, which causes the balloon to rise!

Common Pitfall: Don't forget the order: Heat $\rightarrow$ Expand $\rightarrow$ Less Dense $\rightarrow$ Rise.

This process is governed by Lenz’s Law, which states that the direction of an induced current always opposes the change that caused it.

Why A is correct: When the wire moves down, a current is induced. This current creates its own magnetic field around the wire. This new field interacts with the external magnetic field to produce a force. According to Lenz’s Law, this force must oppose the motion. Since the wire is moving down, the magnetic force must push upward.

Why other answers are incorrect:

• Any statement saying the force is downward is wrong; that would "help" the motion, violating the Law of Conservation of Energy.
• Any statement saying no force is produced is wrong; a current-carrying wire in a magnetic field always experiences a force (the Motor Effect).

Top Tip: Remember "Lenz = Oppose." The induced effect always tries to stop whatever motion started it!

A proton carries a positive charge of relative value +1, while a neutron has no charge at all, so its relative charge is 0.

When a current-carrying wire is placed in a magnetic field, the force it experiences depends on its angle relative to the field lines.

Why it’s correct: Magnetic force is calculated using $F = BIL \sin(\theta)$. When the wire is parallel to the field, the angle ($\theta$) is 0°. Since $\sin(0^\circ) = 0$, the total force becomes zero. Essentially, the current must "cut across" field lines to feel a push; moving along them creates no interaction.

Why other options are wrong:

• Perpendicular (90°): This results in the maximum possible force because the current cuts directly across the field.
• Any other angle (e.g., 45°): This results in a partial force (somewhere between zero and maximum).

Helpful Tip: Think of a person swimming in a river. If you swim with the current (parallel), you don't feel it pushing you sideways. If you try to swim across it (perpendicular), you feel the full force of the water!

EXPLANATION:

Why the correct answer is correct: Conduction is how heat travels through solids. Metals are great conductors because they have free electrons that move quickly, bumping into atoms and transferring energy. However, every metal has a unique atomic structure. Because of these differences, some metals (like copper) allow heat to pass through much faster than others (like steel).

Why other answers are incorrect:

• Uniformity: Any claim that all metals conduct heat at the same rate is false; material type always matters.
• Insulators: Answers suggesting materials like plastic or wood conduct faster than metals are wrong; these are insulators that block heat flow.
• Process: Conduction happens in solids. If an answer mentions "fluids" or "rising air," it is describing convection, not conduction.

Student Tip: When the rods are the same size, the material is the only thing that changes the result.

Common Pitfall: Don’t assume all metals are equal! Always look for the specific material mentioned.

To find the energy in kilowatt-hours (kWh), you must convert the units first:

1. Power: $2000 \text{ W} \div 1000 = \mathbf{2 \text{ kW}}$
2. Time: $15 \text{ minutes} \div 60 = \mathbf{0.25 \text{ hours}}$
3. Energy: $\text{Power} \times \text{Time} = 2 \text{ kW} \times 0.25 \text{ h} = \mathbf{0.5 \text{ kWh}}$

The Fuse: A fuse is a safety device. If the current becomes too high, the wire inside melts and breaks the circuit to prevent overheating or fires.

Why other answers are wrong:

• Incorrect values (like $30,000$ or $500$) usually happen if you forget to convert Watts to kW or minutes to hours.
• A fuse does not "limit" or "smooth" the current; it only acts as a one-time emergency switch that stops the flow entirely.

Common Pitfall: Don’t just multiply $2000 \times 15$. Always check that your units match the final answer requested (kWh)!

Because the transformer is not ideal, you cannot use the current turns-ratio directly; you must work out the real output power across the heater, then scale up to the input power using the 80% efficiency before dividing by the primary voltage to get 0.25 A.

A stable star such as the Sun releases energy by nuclear fusion, joining hydrogen nuclei together to make helium. The other options are fission or chemical reactions, which do not power main-sequence stars.

EXPLANATION:

Why Answer A is Correct: Jupiter is known as the "King of the Planets." It is a gas giant so massive that it contains more than twice the mass of all other planets in our Solar System combined. In terms of size, you could fit over 1,300 Earths inside it!

Why common distractors are wrong:

• "Mercury is the hottest planet": While Mercury is closest to the Sun, Venus is actually the hottest because its thick atmosphere traps heat.
• "Saturn is the largest planet": Saturn has the most spectacular rings, but Jupiter is physically larger and heavier.
• "Mars is larger than Earth": Mars is actually a "miniature" world, only about half the size of Earth.

Helpful Tip: Don’t confuse distance with temperature. The closest planet (Mercury) isn't the hottest. Also, remember that the four outer "Gas Giants" are always much larger than the four inner "Rocky Planets."

In a sticking (inelastic) collision total momentum is conserved, so the initial momentum of the moving truck is shared over the combined mass, giving a smaller common speed of 2.0 m/s.

To find the density, use the formula: Density = Mass ÷ Volume.

1. Find the Volume: The stone's volume is the amount of water it displaces. Subtract the initial water level from the final level: $80\text{ cm}^3 - 50\text{ cm}^3 = \mathbf{30\text{ cm}^3}$.
2. Calculate in g/cm³: Divide the mass by the volume: $120\text{ g} \div 30\text{ cm}^3 = \mathbf{4\text{ g/cm}^3}$.
3. Convert to SI Units: The question asks for the SI unit (kg/m³). To convert g/cm³ to kg/m³, multiply by 1,000: $4 \times 1,000 = \mathbf{4000\text{ kg/m}^3}$.

Why other answers are wrong: Common mistakes include using the initial volume (50) or final volume (80) instead of the difference, or forgetting to convert the units from g/cm³ to kg/m³.

Tip: Always check the required units! If the answer looks too small (like 4), you likely forgot to convert to the SI standard (kg/m³).

Why D is correct: A fuse is a safety device designed to protect the circuit. It contains a thin wire with a low melting point. If the current becomes too high (due to a fault or overload), the wire heats up and melts. This creates a gap in the circuit, which immediately stops the flow of electricity, preventing overheating and potential fires.

Why other answers are wrong:

• Voltage: Fuses do not change or regulate voltage.
• Limiting current: A fuse doesn't "dim" or "turn down" the current; it either allows it to flow normally or cuts it off entirely.
• Switching: While a fuse stops current, it isn't a regular "switch" used to turn appliances on and off.

Helpful Tips:

• Common Pitfall: Students often confuse fuses with circuit breakers. Both stop high current, but a fuse melts and must be replaced, while a breaker can be reset.
• Think of it as a "sacrificial" part: It destroys itself to save the rest of the appliance!

The work done against gravity equals the weight times the height: mgh = 40 x 10 x 5.0 = 2000 J. The time of 2.0 s is not needed for work; it would only matter for power.

EXPLANATION:

The correct answer is 38° because of how we measure angles in physics.

1. The Calculation: The question states the light hits the mirror at 52° to the surface. However, reflection angles are measured from the normal (an imaginary line at 90° to the mirror). To find the angle of incidence, subtract the surface angle from 90°: 90° - 52° = 38°.
2. The Law of Reflection: This law states that the angle of incidence = the angle of reflection. Since the incidence angle is 38°, the reflection angle must also be 38°.

Why other answers are wrong: The most common wrong answer is 52°. This happens if you forget to measure from the normal and mistakenly use the angle to the mirror surface instead.

Top Tip: Always read carefully! If a question mentions the "mirror surface," you must subtract that number from 90° first.

Background-correct both readings before comparing them, use the ratio of corrected rates to extract the half-life, project the corrected rate forward, then add the background back to get what the detector actually shows. Forgetting any one of these steps lands on a wrong option.

Why B is correct: The refractive index ($n$) tells us how much a material slows light down compared to its speed in a vacuum ($c$). The formula for refractive index is $n = \frac{c}{v}$. By rearranging this to solve for the speed in glass ($v$), we get $v = \frac{c}{n}$.

Why the others are wrong:

• $c \times n$: Since $n$ is always greater than 1, multiplying would make light faster than $c$. Nothing travels faster than the speed of light!
• $n / c$: This would give you a tiny decimal that doesn't represent a speed.
• $n + c$: You cannot add a dimensionless ratio ($n$) to a speed ($c$).

Helpful Tip: Always remember that light slows down when it enters a denser medium like glass. Since $n$ is always bigger than 1, dividing $c$ by $n$ is the only way to get a smaller, realistic speed.

To measure mass (the amount of matter in an object), an electronic balance is the correct tool. It provides a precise digital reading, usually in grams or kilograms.

Why the other options are incorrect:

• Rulers are used to measure length, width, or height, not how much an object weighs.
• Graduated cylinders measure volume (the amount of space an object takes up), often by seeing how much water the rock displaces.
• Thermometers measure temperature (how hot or cold something is).

💡 Helpful Tip: Students often confuse mass and volume. Remember:

• Mass = How much "stuff" is inside (use a balance).
• Volume = How much space it fills (use a graduated cylinder).

⚠️ Common Pitfall: Always "tare" or zero your electronic balance before starting! If it doesn't show 0.00 before you begin, your measurement will be wrong.

EXPLANATION:

To find the change in momentum, we use the formula:
$\text{Change in Momentum} = \text{mass} \times (\text{change in velocity})$

Because the mass rebounds, its direction changes. If we treat the initial direction as positive ($+12$ m/s), the rebound direction is negative ($-8$ m/s). The total change in velocity is $12 - (-8) = 20$ m/s.
$\text{Calculation: } 0.50\text{ kg} \times 20\text{ m/s} = \mathbf{10\text{ kg m/s}}$.

Why wrong answers are incorrect:

• 2 kg m/s: This happens if you forget the direction change and subtract the speeds ($12 - 8 = 4$) instead of adding them.
• 6 or 4 kg m/s: These represent only the initial or final momentum, not the difference between them.
• 50 N: This is the force ($10 \div 0.2\text{ s}$), not the momentum.

Top Tip: Always watch for words like "rebound" or "bounce." They signal that you should add the speeds together to find the total change!