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2019年度日本政府(文部科学省)奨学金留学生選考試験

Examination Overview

  • Qualifying Examination for Applicants for the Japanese Government (MEXT) Scholarship 2019

  • Subject: Physics

  • Duration: 60 minutes

Part 1: Examination Instructions

  • Before starting, candidates must fill in personal details: nationality, examination number, name (underline the family name).

  • Instructions for answering questions: Select the correct answer for each question, write the corresponding letters in the answer sheet.

Question 1: Kinematics

Problem Statement:

  1. A car at rest starts moving along a straight line and stops at time t = 80 s.

    • Velocity as a function of time is represented in Fig. 1-1.

    • Find the distance traveled by the car.

    • Options:

      • (a) 5000 m

      • (b) 4000 m

      • (c) 3000 m

      • (d) 2000 m

      • (e) 1000 m

      • (f) 500 m

Figure 1-1 Analysis:

  • Velocity vs. Time Graph highlights the varying speed of the car.

Question 2: Mechanics and Energy

Problem Statement:

  1. A small ball at rest falls from height h and bounces. The coefficient of restitution is e, and gravitational acceleration is g.

    • Find the maximum height after nth impact.

    • Options:

      • (a) he

      • (b) h(1-e)

      • (c) hen

      • (d) he^(2n)

      • (e) he^(2n+2)

      • (f) he^(2n-2)

Question 3: Electromagnetism

Problem Statement:

  1. Two long parallel wires carry current I in opposite directions, at a distance of 2d apart as shown in Fig. 1-2.

    • Find the magnitude of the magnetic field H at point P.

    • Options:

      • (a) 2πα

      • (b) I/(2πd)

      • (c) d/(2πI)

      • (d) 1/(d)I

      • (e) 1/(2d)I

      • (f) 1/d

Figure 1-2 Analysis:

  • Configuration illustrates the magnetic effects due to the currents in parallel wires.

Question 4: Wave Mechanics

Problem Statement:

  1. A sinusoidal wave propagates in the positive x-direction at a speed of 2 m/s. Fig. 1-3 illustrates a snapshot at t = 0.

    • Find the formula for displacement y as a function of t.

    • Options:

      • (a) 2 sin(x - 2t)

      • (b) 3 sin(x^2t)

      • (c) 3 sin(2x-t)

      • (d) 3 sin(2x - 2t)

      • (e) 3 sin(x - t)

      • (f) 3 sin(2xt)

Figure 1-3 Analysis:

  • Snapshot of the wave's displacement across the x-axis.

Question 5: Sound Waves

Problem Statement:

  1. A piston in a tube emits sound waves at a frequency of 555 Hz, causing resonance at distances 14 cm and 44 cm.

    • Find the speed of sound waves.

    • Options:

      • (a) 344 m/s

      • (b) 338 m/s

      • (c) 333 m/s

      • (d) 328 m/s

      • (e) 322 m/s

      • (f) 311 m/s

Part 2: Circuits and Signals

Problem Statement:

  1. Consider the circuit including a resistor R, capacitor C, inductor L, switch S, and battery with voltage V. 1. Find the current I₀ after switch change to position a:

    • Options:

      • (a) CV

      • (b) V/(2R)

      • (c) V/(3R)

      • (d) V/R

      • (e) 0

2. Find charge on capacitor after switch at position a for a long time:

  • Options:

    • (a) C(V + RI₀)

    • (b) C(V - RI₀)

    • (c) CV²

    • (d) CV

    • (e) 0

3. Find Joule heat in resistor when capacitor fully charged:

  • Options:

    • (a) 0

    • (b) (1/2) CV²

    • (c) CV

    • (d) (1/2) CV²

    • (e) CV²

4. Current IL change when switch moves to position c:

  • Graph selections available as options in Fig. 2-2.

5. Find maximum value of Iₗ:

  • Options:

    • (a) V/L

    • (b) V/(2R)

    • (c) √(LC)V

    • (d) 0

Part 3: Kinematics of Projectiles

Problem Statement:

  1. An object of mass m moves with speed v on a frictionless plane.

    • 1. Find the x-coordinate at time t (> 0):

    • Options:

      • (a) vt

      • (b) 2vt

      • (c) vt²

      • (d) vt

      • (e) vt.

    2. Find the y-coordinate when object is in air:

    • Options:

      • (a) h - gt

      • (b) h - gt²

      • (c) -gt²

      • (d) h

      • (e) h + (-gt²)

3. Failure to hit slope condition based on speed:

  • Options:

    • (a) √(2gh)/tan(θ)

    • (b) √2gh

    • (c) 2√(gh)

    • (d) √gh/2

Part 4: Thermodynamics and Gas Laws

Problem Statement:

  1. Non-adiabatic cylinder dynamics with ideal gas. Factors include:

    • Height changes and corresponding expressions for height:

      • (1) Find expression of height h₁ after weight M placed on piston.

      • Options:

      • (a) h

      • (b) h(PA + (Mm)g)

      • (c) h(PA + mg)

    • 2. Work done during height change from h to h₁:

      • Options:

      • (a) 0

      • (b) PA + Mg

      • (c) PA + mg

3. Temperature of gas after mass removal from piston:

  • Options:

    • (a) T

    • (b) h₂ + h₁

    • (c) Specific expressions based on pressure.

4. Final height h₃ after gas expansion:

  • Options:

    • (a) h

    • (b) h/2

    • (c) 2h2

    • (d) h

Part 5: Optics and Interference

Problem Statement:

  1. A ray of light of wavelength λ travels through a soap film of thickness d.

    • 1. Find the wavelength of light in the film:

    • Options:

      • (a) λ/n

      • (b) nλ

      • (c) √(n)λ

2. Relationship between angles:

  • Options:

    • (a) sinθinternal = n sinθexternal

    • (b) cosθinternal = n² cosθexternal

3. Condition for constructive interference:

  • Options:

    • (a) Relationship on path lengths for integer m.

4. Expression for thickness d under constructive condition:

  • Options:

    • (a) mλ/(2n) adjustments for thickness due to interference.