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 uniform chain of mass

M

and length

L

lies on a frictionless horizontal table, with a length

L/3

hanging over the edge. The chain is released from rest. What is its speed at the moment the last link leaves the table?

A. $\sqrt{\tfrac{2gL}{3}}$
B. $\tfrac{2}{3}\sqrt{2gL}$
C. $\sqrt{gL}$
D. $\tfrac13\sqrt{2gL}$
E. $\sqrt{\tfrac{8gL}{3}}$

Answer: B

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Question 2

1 mark

Twelve identical

6.0\,\Omega

resistors are soldered along the twelve edges of a cube. What is the resistance between two diametrically opposite corners?

A. $2.0\,\Omega$
B. $3.5\,\Omega$
C. $4.5\,\Omega$
D. $5.0\,\Omega$
E. $7.2\,\Omega$

Answer: D

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Question 3

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 4

1 mark

In a two-slit interference experiment with light of wavelength

600\,\text{nm}

, a thin film of refractive index

1.5

is placed over one slit. The central bright fringe moves to the position previously occupied by the fifth bright fringe. What is the thickness of the film?

A. $12\,\mu\text{m}$
B. $2.0\,\mu\text{m}$
C. $4.0\,\mu\text{m}$
D. $9.0\,\mu\text{m}$
E. $6.0\,\mu\text{m}$

Answer: E

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Question 5

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 6

1 mark

A cell of constant emf and internal resistance

r

is connected to a variable resistor

R

. The power dissipated in

R

is found to be the same when

R=2.0\,\Omega

as when

R=8.0\,\Omega

. What is

r

A. $2.0\,\Omega$
B. $3.0\,\Omega$
C. $4.0\,\Omega$
D. $5.0\,\Omega$
E. $6.0\,\Omega$

Answer: C

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Question 7

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 8

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 9

1 mark

A block of ice with a small steel ball frozen inside it floats in a beaker of water. The ice melts completely, and the ball sinks to the bottom. What happens to the water level in the beaker?

A.It rises.
B.It falls.
C.It is unchanged.
D.It rises while the ice melts, then returns to its original level.
E.It depends on the density of the steel.

Answer: B

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Question 10

1 mark

A car of mass

1200\,\text{kg}

has a maximum speed of

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

climbing a hill of gradient

1

20

(that is,

\sin\theta = 1/20

), against a constant resistive force of

400\,\text{N}

. Working at the same rate on level ground, against the same resistive force, what is its maximum speed?

A. $40\,\text{m s}^{-1}$
B. $25\,\text{m s}^{-1}$
C. $30\,\text{m s}^{-1}$
D. $50\,\text{m s}^{-1}$
E. $60\,\text{m s}^{-1}$

Answer: D

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