2019 MEXT Gakubu Physics

24 Nov

2019 MEXT Gakubu Physics

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Part 1

QUESTION 01

A car at rest starts moving along a straight line and stops at time t = 80 s. The velocity v of the car changes as a function of time t as shown in Fig below. Find the distance that the car travels.

(A) 5000 m

(B) 4000 m

(D) 2000 m

(E) 1000 m

(F) 500 m

Solution

QUESTION 02

A small ball at rest falls down from a height of h above the ground and bounces repeatedly. The coefficient of restitution between the ball and the ground is denoted as e, and the acceleration of gravity as g. Find the maximum height of the ball between the nth and the (n+1)th impact with the ground.

(A) \(he\)

(B) \(h(1 - e)^n\)

(D) \(he^{2n}\)

(E) \(he^{2n+2}\)

(F) \(he^{2n-2}\)

Solution

QUESTION 03

Two long straight wires with the same current I flowing in the opposite direction, are placed parallel to each other with a distance of 2d as shown in Fig. below. Find the magnitude of magnetic field H at point P.

(A) \(\dfrac {I}{2 \pi d}\)

(B) \(\dfrac {I}{\pi d}\)

(D) \(\dfrac {2 \pi I}{d}\)

(E) \(\dfrac {I}{d}\)

(F) \(\dfrac {I}{2d}\)

Solution

QUESTION 04

A sinusoidal wave travels in the positive x-direction with a constant speed of 2 m/s. Figure below shows a snapshot of the wave at t = 0 s as a function of x. Find the formula for the displacement y at time t.

(A) \(2 \sin \pi (x - 2t)\)

(B) \(3 \sin \dfrac {\pi}{2} (x - 2t)\)

(D) \(3 \sin \dfrac {\pi}{2} (2x - t)\)

(E) \(3 \sin \pi (x - t)\)

(F) \(3 \sin \dfrac {\pi}{4} (2x - t)\)

Solution

QUESTION 05

A movable piston is fitted in a tube as shown in Fig. below. A speaker near the open end of the tube emits sound waves with a frequency of 555 Hz. When the piston moves from the left end to the right, the first and second resonances are produced at distances 14 cm and 44 cm from the open end, respectively. Find the speed of the sound waves.

(A) 344 m/s

(B) 338 m/s

(D) 328 m/s

(E) 322 m/s

(F) 311 m/s

Solution