NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Waves, Sound, Optics and Thermodynamics (Set 4): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A particle in SHM starts from the equilibrium position at t = 0. What fraction of the period T passes before it first reaches a displacement equal to half the amplitude?
Answer: B. T/12
Explanation: x = A sin(2πt/T) = A/2 gives 2πt/T = π/6, so t = T/12. (T/6 is the time to go from the equilibrium position to x = A·√3/2.)
Q2. A mass hanging from a spring oscillates with a period of 2.0 s. The spring is cut into two equal halves and the same mass is hung from one half. What is the new period?
Answer: A. 1.41 s
Explanation: Halving the length doubles the spring constant (k ∝ 1/length). T ∝ 1/√k, so T = 2.0/√2 = 1.41 s.
Q3. A simple pendulum clock is in a lift that accelerates upward at g/3. What is the ratio of its period to the period when the lift is at rest?
Answer: B. 0.866
Explanation: Effective gravity g_eff = g + g/3 = 4g/3, and T ∝ 1/√g_eff, so T'/T = √(3/4) = 0.866; the clock runs fast.
Q4. A particle in SHM of amplitude A passes through the point x = A/2. What fraction of its maximum speed does it have there?
Answer: B. 0.866
Explanation: v = ω√(A² − x²) = ωA√(1 − ¼) = (√3/2) ωA = 0.866 v_max. At x = A/√2 the speed would be 0.707 v_max.
Q5. A transverse sinusoidal wave of amplitude 1.0 mm and wavelength 10 cm travels along a string. What is the ratio of the maximum particle speed to the wave speed?
Answer: C. 0.063
Explanation: v_max/v = Aω/(ω/k) = Ak = 2πA/λ = 2π × 1 × 10⁻³/0.10 = 0.063. Particle speed and wave speed are different things.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. The sound intensity level at 2.0 m from a small source is 80 dB. Assuming a point source radiating equally in all directions with no absorption, what is the level at 8.0 m?
Q7. One machine produces a sound intensity level of 60 dB at a point. What is the level when two identical machines operate together at the same distance?
Q8. The speed of sound in air at 27 °C is 340 m s⁻¹. What is it at 327 °C, assuming it varies as √T?
Q9. A stationary siren emits a note of 400 Hz toward a car approaching at 20 m s⁻¹, and the sound reflects from the car back to the siren (speed of sound 340 m s⁻¹). What frequency does the siren operator hear in the reflected sound?
Q10. A string 60 cm long is fixed at both ends and vibrates in its third harmonic at 300 Hz. What is the speed of waves on the string?
Q11. In a resonance tube experiment with a 500 Hz fork, the first and second resonances occur at air-column lengths of 16.5 cm and 50.5 cm. What are the speed of sound and the end correction?
Q12. A tuning fork of known frequency 256 Hz produces 4 beats per second with an unknown fork. After loading the unknown fork with a little wax, the beat frequency falls to 2 beats per second. What was the frequency of the unknown fork?
Q13. A non-reflective coating of MgF₂ (refractive index 1.38) is deposited on glass of higher index. What is the minimum coating thickness that cancels reflection of light of wavelength 552 nm in air?
Q14. In Young's double-slit experiment λ = 600 nm, slit separation 0.30 mm and screen distance 1.5 m. What is the fringe width when the whole apparatus is immersed in water (refractive index 4/3)?
Q15. Light of wavelength 500 nm falls on a single slit of width 2.0 μm. At what angle does the first diffraction minimum appear?
Q16. What is the minimum angular separation that can be resolved by a lens of aperture 10 cm at λ = 550 nm, using the Rayleigh criterion θ = 1.22 λ/D?
Q17. Unpolarised light of intensity I₀ passes through two ideal polarisers whose transmission axes are at 60° to each other. What is the transmitted intensity?
Q18. A fish is 1.2 m below the surface of still water (refractive index 4/3). At what depth does it appear to be to an observer looking vertically down?
Q19. An equilateral prism of refractive index √2 is set at minimum deviation. What is the angle of minimum deviation?
Q20. A biconvex lens with both radii 20 cm has refractive index 1.5 and focal length 20 cm in air. What is its focal length when fully immersed in water (n = 4/3)?
Q21. A concave mirror has radius of curvature 40 cm. An object is placed 30 cm in front of it. What is the image distance and magnification?
Q22. An astronomical telescope in normal adjustment has an objective of focal length 100 cm and an eyepiece of focal length 5.0 cm. What are its angular magnification and tube length?
Q23. Two moles of an ideal gas expand isothermally at 300 K until the volume doubles. How much heat does the gas absorb? (R = 8.314 J K⁻¹ mol⁻¹, ln 2 = 0.693)
Q24. A diatomic ideal gas (γ = 1.4) at 300 K is compressed adiabatically to one-eighth of its initial volume. What is the final temperature? (8^0.4 = 2.297)
Q25. A real engine operating between 600 K and 300 K achieves 60% of the Carnot efficiency. How much work does it do for 5000 J of heat absorbed from the hot reservoir?
Q26. How much heat is needed to raise the temperature of 2 mol of a diatomic ideal gas (translation and rotation only) by 10 K at constant pressure? (R = 8.314 J K⁻¹ mol⁻¹)
Q27. What is the internal energy of 1 mol of a diatomic ideal gas at 300 K, counting only translational and rotational motion? (R = 8.314 J K⁻¹ mol⁻¹)
Q28. Two rods of identical length and cross-section are joined end to end. Their thermal conductivities are 2k and k. The free end of the first is held at 100 °C and that of the second at 0 °C. What is the steady-state temperature at the junction?
Q29. A steel rod (Y = 2.0 × 10¹¹ Pa, α = 12 × 10⁻⁶ K⁻¹) is clamped rigidly between two walls at 20 °C so it cannot expand. What stress develops when it is heated to 70 °C?
Q30. 100 g of ice at 0 °C is added to 200 g of water at 60 °C in an insulated container. (Latent heat of fusion 334 J g⁻¹, specific heat of water 4.18 J g⁻¹ K⁻¹.) What is the final temperature?