NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Waves, Sound, Optics and Thermodynamics (Set 5): 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 executes SHM with period 2.4 s starting from the equilibrium position. How long does it take to reach a displacement equal to half the amplitude for the first time?
Answer: D. 0.20 s
Explanation: x = A sin(2πt/T). x = A/2 gives 2πt/T = π/6, so t = T/12 = 2.4/12 = 0.20 s.
Q2. A block attached to a spring oscillates with frequency f. The same spring is cut into two equal halves and the same block is attached to one half. What is the new frequency?
Answer: A. √2 f
Explanation: A half-length spring is twice as stiff (k ∝ 1/length), so k′ = 2k. Frequency f ∝ √k, so f′ = √2 f.
Q3. A pendulum clock keeps correct time at sea level. At a mountain top, g is lower by 0.020%. About how much time does the clock lose per day? (Period T ∝ g^(−½); 1 day = 86 400 s)
Answer: C. 8.6 s
Explanation: ΔT/T = ½ × Δg/g = 0.010%. Over a day the clock runs slow by 1.0 × 10⁻⁴ × 86 400 = 8.64 s.
Q4. A string of mass 5.0 g and length 1.0 m is stretched to a tension of 20 N and clamped at both ends. What is the frequency of its second overtone (third harmonic)? (Wave speed v = √(T/μ), μ = mass per unit length.)
Answer: B. 95 Hz
Explanation: μ = 0.0050 kg m⁻¹, so v = √(20/0.0050) = 63.2 m s⁻¹. Fundamental f₁ = v/2L = 31.6 Hz. The third harmonic = 3 × 31.6 = 94.9 Hz.
Q5. A travelling wave is described by y = 0.020 sin(5π x − 300π t), with x and y in metres and t in seconds. What are the wave speed and its direction of travel?
Answer: D. 60 m s⁻¹ in the +x direction
Explanation: v = ω/k = 300π/5π = 60 m s⁻¹. The argument (kx − ωt) indicates travel in the +x direction.
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Q6. At what displacement from equilibrium (as a fraction of the amplitude A) are the kinetic and potential energies of a harmonic oscillator equal?
Q7. A tuning fork produces a 1700 Hz note in air. If the same note travels into water, what is its wavelength there? (Speed of sound: 340 m s⁻¹ in air, 1480 m s⁻¹ in water.)
Q8. A car travelling at 20 m s⁻¹ toward a large flat wall sounds its horn at 1000 Hz. What frequency does the driver hear in the echo from the wall? (Speed of sound = 340 m s⁻¹)
Q9. A small loudspeaker radiates 1.0 W of sound uniformly in all directions in an open field. Taking the threshold intensity as 1.0 × 10⁻¹² W m⁻², what is the sound intensity level at a distance of 10 m?
Q10. Two identical machines each produce a sound level of 60 dB at a listener's position when running alone. What is the level when both run together?
Q11. In a Young's double-slit experiment in air the fringe width is 1.20 mm. The entire apparatus is immersed in water of refractive index 1.33. What is the new fringe width?
Q12. Light of wavelength 500 nm passes through a single slit 0.10 mm wide and falls on a screen 2.0 m away. What is the width of the central maximum on the screen? (Use small angles; width = 2λD/a.)
Q13. Unpolarised light of intensity I₀ passes through a polariser P₁, then through a polariser P₂ at 45° to P₁, then through P₃ at 90° to P₁ (45° to P₂). What is the final intensity?
Q14. A fish is 3.0 m below the surface of still water (n = 4/3). To an observer looking vertically down from above, how deep does it appear to be?
Q15. A thin biconvex lens of refractive index 1.50 has both faces of radius 20 cm, so its focal length in air is 20 cm. What is its focal length when completely immersed in water (n = 1.33)?
Q16. An object is 20 cm from a convex (diverging) mirror of focal length −20 cm. Using the real-is-positive convention (real images positive, virtual images negative, f negative for a convex mirror), what are the image distance v and the magnification m?
Q17. A prism of refracting angle 60° has refractive index √3. What is its angle of minimum deviation?
Q18. A compound microscope has an objective of focal length 1.0 cm and an eyepiece of focal length 5.0 cm, with the lenses 20 cm apart (tube length L = 20 cm, use M ≈ (L/f_o)(D/f_e) with D = 25 cm for final image at infinity). What is the angular magnification?
Q19. A hypermetropic person has a near point at 50 cm. What power of spectacle lens allows comfortable reading at the normal distance of 25 cm? (Image formed at the near point, 50 cm.)
Q20. Two moles of an ideal gas expand isothermally at 300 K to three times their initial volume. Using R = 8.314 J mol⁻¹ K⁻¹, what work do they do?
Q21. A monatomic ideal gas (γ = 5/3) at 300 K is compressed adiabatically and reversibly to ⅛ of its original volume. What is its final temperature?
Q22. A refrigerator works between an interior at 270 K and a room at 300 K. Assuming it is ideal (Carnot), what is the minimum power required to remove heat from the interior at the rate of 900 J s⁻¹?
Q23. What heat is needed to raise the temperature of 2.0 mol of a diatomic ideal gas (rigid rotor, Cp = 7R/2) by 10 K at constant pressure? (R = 8.314 J mol⁻¹ K⁻¹)
Q24. Air at standard conditions has density 1.2 kg m⁻³ and r.m.s. molecular speed about 500 m s⁻¹. Using the kinetic theory result P = ⅓ρ⟨v²⟩, what pressure does this give?
Q25. A copper rod (k = 400 W m⁻¹ K⁻¹) and a steel rod (k = 50 W m⁻¹ K⁻¹), of equal length and cross-section, are joined end to end. The free end of copper is held at 100 °C and the free end of steel at 0 °C. What is the temperature of the junction in steady state?
Q26. A steel plate has a circular hole of diameter 2.00 cm. When the plate is heated uniformly, what happens to the diameter of the hole?
Q27. 100 g of water at 80 °C is mixed with 50 g of ice at 0 °C in an insulated container. Take c(water) = 4.18 J g⁻¹ K⁻¹ and L_fusion = 334 J g⁻¹. What is the final temperature?
Q28. A black sphere of radius 0.10 m at 500 K is in surroundings at 300 K. Using σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ and emissivity 1, what is its net rate of heat loss by radiation?
Q29. A gas is taken around a rectangular cycle on a P–V diagram: pressure ranges from 1.0 × 10⁵ Pa to 3.0 × 10⁵ Pa and volume from 2.0 × 10⁻³ m³ to 4.0 × 10⁻³ m³, traversed clockwise. What is the net work done by the gas per cycle?
Q30. A person loses heat by evaporating 50 g of sweat at body temperature. The latent heat of vaporisation is 2.42 kJ g⁻¹. If this heat is removed from a 60 kg body of average specific heat 3.5 kJ kg⁻¹ K⁻¹, by how much does the body temperature fall?