ESAT Challenge Physics Esat-physics-challenge-2

10 questions10 marks20Updated August 2026

The ESAT Challenge Physics Esat-physics-challenge-2 paper in full: all 10 questions, each with its answer. ESAT is the Engineering and Science Admissions Test. Sit it cold under exam timing, mark it, then work back through anything you missed using the solutions below.

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Question 1

1 mark

A single

50\,\text{g}

ice cube at

0\,^\circ\text{C}

is dropped into a vacuum flask holding

200\,\text{g}

of a drink at

30\,^\circ\text{C}

. Treat the drink as water and the flask as perfectly insulating. Specific latent heat of fusion of ice

=336\,\text{J g}^{-1}

; specific heat capacity of water

=4.2\,\text{J g}^{-1}\,\text{K}^{-1}

. What is the final temperature?

A. $4\,^\circ\text{C}$
B. $8\,^\circ\text{C}$
C. $0\,^\circ\text{C}$
D. $6\,^\circ\text{C}$
E. $12\,^\circ\text{C}$

Answer: B

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Question 2

1 mark

A small light ball rests on top of a much heavier ball, the two just touching. The pair is released from rest so that the heavy ball falls a height

h

to the floor. All collisions are perfectly elastic and air resistance is negligible. To what maximum height above the floor does the small ball rise?

A. $4h$
B. $3h$
C. $9h$
D. $h$
E. $16h$

Answer: C

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Question 3

1 mark

A safety officer checks a sealed gamma source that emits

8.0\times10^{5}

photons per second, uniformly in all directions. A detector with a window of area

5.0\,\text{cm}^2

is held

2.0\,\text{m}

away, facing the source. Assuming every photon entering the window is counted and that absorption in air is negligible, what count rate is recorded?

A. $8\,\text{s}^{-1}$
B. $2\,\text{s}^{-1}$
C. $4\,\text{s}^{-1}$
D. $16\,\text{s}^{-1}$
E. $40\,\text{s}^{-1}$

Answer: A

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Question 4

1 mark

A sphere falling through air at high speed experiences a drag force

F = k\rho A v^2

, where

A

is its cross-sectional area and

k

is a dimensionless constant. Two solid spheres are made of the same material, one of twice the radius of the other. By what factor is the terminal speed of the larger sphere greater than that of the smaller?

A. $1$
B. $\sqrt{2}$
C. $2$
D. $2\sqrt{2}$
E. $4$

Answer: B

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Question 5

1 mark

A small generator produces

20\,\text{kW}

of electrical power at

200\,\text{V}

. This is fed into the primary coil of a transformer that has

250

turns on the primary and

5000

turns on the secondary. The secondary is connected to a village by a cable of total resistance

0.50\,\Omega

.

The transformer transfers all of the power supplied to it.

What power is wasted as heat in the cable?

A. $2.5\,\text{W}$
B. $12.5\,\text{W}$
C. $50\,\text{W}$
D. $5.0\,\text{kW}$
E. $2.0\,\text{MW}$

Answer: B

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Question 6

1 mark

A bubble of air of volume

12\,\text{mm}^3

is released from the bottom of a lake of depth

20\,\text{m}

. It rises slowly, and its temperature does not change on the way up.

Atmospheric pressure is

100\,\text{kPa}

, the density of the water is

1000\,\text{kg m}^{-3}

and the gravitational field strength is

10\,\text{N kg}^{-1}

.

What is the volume of the bubble when it is halfway to the surface?

A. $6.0\,\text{mm}^3$
B. $8.0\,\text{mm}^3$
C. $12\,\text{mm}^3$
D. $18\,\text{mm}^3$
E. $24\,\text{mm}^3$
F. $36\,\text{mm}^3$

Answer: D

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Question 7

1 mark

A car is travelling along a straight road at

20\,\text{m s}^{-1}

. The driver sees a hazard, and after a reaction time of

0.60\,\text{s}

applies the brakes, after which the car decelerates uniformly at

5.0\,\text{m s}^{-2}

until it stops. The car travels at a constant speed during the reaction time.

The same car, driven by the same driver and braking in the same way, now travels at

30\,\text{m s}^{-1}

.

By how much does the total distance travelled between seeing the hazard and stopping increase?

A. $26\,\text{m}$
B. $50\,\text{m}$
C. $56\,\text{m}$
D. $65\,\text{m}$
E. $106\,\text{m}$
F. $108\,\text{m}$

Answer: C

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Question 8

1 mark

A freshly prepared sample contains

8.0 \times 10^{20}

atoms of a radioactive nuclide X and no atoms of anything else. X has a half-life of

12

days and decays to a stable nuclide Y.

Which row gives the time at which the sample first contains three times as many atoms of Y as of X, and the number of atoms of Y present at that time?

A.time: $12$ days, atoms of Y: $4.0 \times 10^{20}$
B.time: $24$ days, atoms of Y: $2.0 \times 10^{20}$
C.time: $24$ days, atoms of Y: $6.0 \times 10^{20}$
D.time: $36$ days, atoms of Y: $6.0 \times 10^{20}$
E.time: $36$ days, atoms of Y: $7.0 \times 10^{20}$
F.time: $48$ days, atoms of Y: $7.5 \times 10^{20}$

Answer: C

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Question 9

1 mark

A spring obeys Hooke's law throughout the range considered here. A force of

6.0\,\text{N}

stretches it by

4.0\,\text{cm}

.

How much additional work must be done to stretch the spring from an extension of

4.0\,\text{cm}

to an extension of

8.0\,\text{cm}

A. $0.12\,\text{J}$
B. $0.24\,\text{J}$
C. $0.36\,\text{J}$
D. $0.48\,\text{J}$
E. $0.96\,\text{J}$

Answer: C

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Question 10

1 mark

12\,\text{V}

supply of negligible resistance is connected in series with a fixed resistor of resistance

2.0\,\text{k}\Omega

, an NTC thermistor and an ammeter.

With the thermistor at

20\,^\circ\text{C}

the ammeter reads

1.5\,\text{mA}

. The thermistor is then heated to

60\,^\circ\text{C}

, at which its resistance is one sixth of its value at

20\,^\circ\text{C}

.

Which row gives the ammeter reading at

60\,^\circ\text{C}

and the power dissipated in the fixed resistor at

60\,^\circ\text{C}

A.ammeter reading: $1.0\,\text{mA}$ , power in fixed resistor: $2.0\,\text{mW}$
B.ammeter reading: $1.5\,\text{mA}$ , power in fixed resistor: $4.5\,\text{mW}$
C.ammeter reading: $1.5\,\text{mA}$ , power in fixed resistor: $18\,\text{mW}$
D.ammeter reading: $4.0\,\text{mA}$ , power in fixed resistor: $16\,\text{mW}$
E.ammeter reading: $4.0\,\text{mA}$ , power in fixed resistor: $32\,\text{mW}$
F.ammeter reading: $4.0\,\text{mA}$ , power in fixed resistor: $48\,\text{mW}$
G.ammeter reading: $6.0\,\text{mA}$ , power in fixed resistor: $72\,\text{mW}$
H.ammeter reading: $9.0\,\text{mA}$ , power in fixed resistor: $162\,\text{mW}$

Answer: E

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