Full Exam Quiz

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)