Physics Oxbridge Interview Questions
Twenty genuine-difficulty physics questions, each with a clear diagram and an optional hint, written and illustrated by our Oxbridge-graduate tutors.
Question 1
A tennis ball is balanced on top of a basketball and the two are dropped together from rest. How high does the tennis ball bounce?
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Treat the two impacts in sequence. The basketball strikes the floor and reverses first, then collides with the still-descending tennis ball. Work in the basketball's frame at that instant and apply conservation of momentum and energy for a light ball rebounding off a much heavier one. See what multiple of the impact speed the tennis ball can leave with, then turn that speed back into a height.
Question 2
An ice cube floats in a glass of water filled to the brim. When it melts, does the water overflow, drop, or stay level?
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A floating object displaces its own weight in water. Compare the volume of water the floating ice pushes aside with the volume of water it produces once it has melted. Ask whether those two volumes are the same, and what the change in density from ice to water implies.
Question 3
A bungee jumper of mass m steps off a platform on a rope of natural length L and stiffness k, above a pit a distance H below. What’s the longest rope that keeps them safe?
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Use energy conservation between the platform and the lowest point: gravitational PE lost equals elastic PE stored in the rope. The rope only begins to stretch once the fall exceeds its natural length L, so express the extension in terms of the total drop. For the limiting case, set the lowest point exactly at the pit floor (depth H) and solve for L.
Question 4
Drill a tunnel straight through the centre of the Earth and drop a ball in. Describe its motion and find the time to reach the other side.
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Inside a uniform sphere, only the mass closer to the centre than you pulls you inward, so the gravitational force grows in proportion to your distance from the centre. A restoring force proportional to displacement is the signature of simple harmonic motion. Identify the effective "spring constant," write down the period, and remember the one-way journey is half of it.
Question 5
If the Earth were suddenly stopped in its orbit, how long would it take to fall into the Sun?
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Treat the straight fall as an extremely thin, collapsed ellipse with the Sun at one focus, so its semi-major axis is half the original orbital radius. Apply Kepler's third law to relate this degenerate orbit's period to Earth's actual year, then note that the fall is only half of that period.
Question 6
Do you weigh more at the North Pole or at the equator?
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Two effects act at the equator that don't at the pole. First, a point on the equator is moving in a circle as the Earth spins, so part of gravity must be "used up" providing the centripetal force, leaving less to register as weight. Second, the equatorial bulge places you slightly further from the centre. Consider which way each effect pushes the reading.
Question 7
Twelve identical resistors R form the edges of a cube. What’s the resistance between two diagonally opposite corners?
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Don't try to solve the full network. Use symmetry instead. By the symmetry of the cube about the diagonal joining A and B, several corners must sit at exactly the same potential. Mentally join those equal-potential points together and the twelve resistors collapse into a short chain of simple parallel groups.
Question 8
Estimate the total mass of the Earth’s atmosphere.
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Atmospheric pressure at the surface is just the weight of the air column above each unit of area, divided by that area. Rearrange to get the total weight of the atmosphere from the surface pressure and the Earth's surface area, then divide by g for the mass. You'll need the Earth's radius and standard atmospheric pressure.
Question 9
Roughly how high could you climb on the energy in a single chocolate bar?
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Equate the usable chemical energy in the bar to the gravitational PE you gain, mgh. Estimate the bar's energy (a label gives roughly 1000 kJ), your own mass, and the step people forget: the efficiency with which muscles convert food energy into height, which is only about a fifth. State each assumption as you make it.
Question 10
A sand timer is placed on a sensitive scale and flipped. Does the reading stay constant while the sand runs through?
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Force is the rate of change of momentum, so you must account for all the sand, not just what's resting. During steady flow, the weight of the airborne sand "missing" from the reading is balanced by the impulse of sand landing. The interesting part is the very start and very end, before steady flow begins and after it stops.
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Talk to us about interview preparationQuestion 11
A slinky is held by its top end so it hangs at rest, then released. What does the bottom of the slinky do in the instant after release?
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Look at the forces on the bottom coil the instant after release. Just before, it was in equilibrium, its weight balanced by the stretched coils above pulling up. That upward tension cannot vanish instantly; it persists until the collapsing top reaches the bottom. Then ask separately what the centre of mass of the whole slinky must be doing.
Question 12
A satellite in low orbit experiences a tiny amount of atmospheric drag. Does it speed up or slow down?
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Keep speed and energy separate. For a circular orbit, the orbital speed is fixed by the radius, while the total energy is negative and grows in magnitude as the orbit shrinks. Drag removes energy, so the orbit drops to a smaller radius. Now work out what that smaller radius does to the speed.
Question 13
A charged capacitor is connected across an identical uncharged one. Compare the total stored energy before and after. Anything surprising?
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Charge is conserved when the switch closes, so find the shared final voltage from the total charge spread across the combined capacitance. Then compare the energy ½CV² before and after. You'll find some has gone missing, and the rewarding part is identifying exactly where it went.
Question 14
An infinite ladder network is built from identical resistors R: a series R, then a parallel R to the rail, repeating forever. What is the total resistance?
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Exploit self-similarity: the network beyond the first section is identical to the whole thing. Call the total resistance X, then redraw just the first series-R and parallel-R with a single resistor "X" standing in for everything that follows. That lets you write X in terms of itself, giving a quadratic to solve.
Question 15
A uniform chain is held vertically with its lower end just touching a table, then released. What force does the chain exert on the table when a length has piled up?
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Two contributions add at the table: the weight of the chain already lying on it, plus the force needed to halt the links still arriving. Use force as the rate of change of momentum for the arriving chain (mass per unit length times speed, times speed again), and relate that speed to the distance already fallen. Compare the total with the resting weight alone.
Question 16
A cylindrical buoy floating upright is pushed down slightly and released. Describe its motion and find the period.
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Push the buoy down by a small distance x and find the extra upward force. It's the weight of the additional water displaced, which is proportional to x. A restoring force proportional to displacement means simple harmonic motion, so read off the effective "spring constant" from the cross-sectional area and the water density, then write the period.
Question 17
A ball dropped from height h₀ has coefficient of restitution e at each bounce. Find the total distance it travels and the total time before it stops.
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A coefficient of restitution e means each bounce returns the ball to e² times the previous height, since height depends on speed squared. The successive heights then form a geometric series, so sum it for the total distance, taking care with the very first drop. For the total time, find the duration of each up-and-down and sum that geometric series too.
Question 18
A raindrop falls through a stationary cloud, sweeping up mist and growing as it goes. Show that it can fall with constant acceleration, and find it.
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Write Newton's second law in its full form, force equals the rate of change of momentum, with the mass increasing as the drop sweeps up mist, so the growth rate depends on the drop's size and speed. Then look for a self-similar solution in which the acceleration is constant: substitute it in and find which constant acceleration is consistent with the equations.
Question 19
A massless rope passes over a frictionless pulley. A monkey holds one end; a bunch of bananas of exactly equal weight balances it on the other. The monkey starts climbing. What happens to the bananas?
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The tension is the same on both sides of the rope and the two masses are equal. Apply Newton's second law to the monkey and to the bananas separately: any extra pull the monkey exerts to climb is transmitted equally, through the tension, to the bananas. Compare their accelerations, and keep Newton's third law firmly in mind.
Question 20
You’re in a boat on a small pond, holding a heavy rock. You throw the rock into the water. Does the water level at the edge of the pond rise, fall, or stay the same?
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Compare two states. While in the boat, the rock floats via the boat and so displaces its own weight in water; once on the bottom, it displaces only its own volume. Since the rock is denser than water, decide which of those displacements is larger, and that tells you which way the level moves.
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