NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Waves, Sound, Optics and Thermodynamics (Set 6): 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 0.30 kg mass is attached to two light springs of force constants 200 N m⁻¹ and 300 N m⁻¹ joined end to end (in series), and oscillates on a frictionless horizontal surface. What is its period?
Answer: D. 0.31 s
Explanation: For springs in series, 1/k = 1/200 + 1/300, so k = 120 N m⁻¹. T = 2π√(m/k) = 2π√(0.30/120) = 0.31 s. (Springs in parallel, k = 500, would give 0.15 s.)
Q2. A mass hung on a vertical light spring stretches it by 4.9 cm at equilibrium. If the mass is pulled down slightly and released, what is its period of oscillation? (g = 9.8 m s⁻²)
Answer: D. 0.44 s
Explanation: At equilibrium mg = kx, so m/k = x/g. T = 2π√(m/k) = 2π√(0.049/9.8) = 2π × 0.0707 = 0.44 s.
Q3. A 0.50 kg block on a frictionless table is attached to a spring of force constant 200 N m⁻¹ and set oscillating with amplitude 0.10 m. What is its speed as it passes through the equilibrium position?
Answer: C. 2.0 m s⁻¹
Explanation: Energy: ½kA² = ½mv²max, so vmax = A√(k/m) = 0.10 × √(200/0.50) = 0.10 × 20 = 2.0 m s⁻¹.
Q4. A source of 1000 Hz travels at 20 m s⁻¹ along a straight road, chasing an observer who moves in the same direction at 10 m s⁻¹ ahead of it. The speed of sound is 340 m s⁻¹ and there is no wind. What frequency does the observer hear?
Answer: C. 1031 Hz
Explanation: Both move in the same direction (source behind the observer). f′ = f(v − v_o)/(v − v_s) = 1000 × (340 − 10)/(340 − 20) = 1000 × 330/320 = 1031 Hz.
Q5. A wave of frequency 200 Hz travels at 120 m s⁻¹. What is the phase difference between two points on the wave 0.15 m apart along its direction of travel?
Answer: B. π/2 rad
Explanation: λ = v/f = 120/200 = 0.60 m. Phase difference = 2πΔx/λ = 2π × 0.15/0.60 = π/2 rad.
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Q6. In Melde's experiment a driven string vibrates in 4 loops at a fixed driving frequency. By what factor must the tension be changed to make it vibrate in 2 loops at the same frequency?
Q7. In an ultrasound scan, a pulse sent into tissue returns after reflection from an organ boundary 40 µs later. If the speed of sound in tissue is 1540 m s⁻¹, how deep is the boundary?
Q8. At the same temperature, what is the ratio of the speed of sound in hydrogen (M = 2) to that in oxygen (M = 32)? Treat both as ideal diatomic gases with the same γ.
Q9. A thin biconvex glass lens (n = 1.5) has a focal length of 20 cm in air. What is its focal length in water (n = 4/3)?
Q10. A ray enters one short face of a right-angled isosceles glass prism (n = 1.5) at normal incidence and strikes the long (hypotenuse) face. What happens there?
Q11. A thin glass prism of refracting angle 5° has refractive indices 1.50 for red light and 1.52 for violet light. What is the angular dispersion between these colours? (δ = (n − 1)A for a thin prism)
Q12. A thin film of oil (n = 1.40) floats on water (n = 1.33) and is viewed in air at near-normal incidence. Light of wavelength 560 nm (in air) is strongly reflected. What is the minimum non-zero film thickness for this?
Q13. A diffraction grating has 5000 lines per cm and is illuminated normally with light of wavelength 600 nm. How many bright maxima (including the central one) can be observed?
Q14. At what angle of incidence is light reflected from a glass surface (n = 1.5) in air completely plane polarised?
Q15. An optical fibre has a core of refractive index 1.50 and cladding of index 1.45. What is the maximum acceptance angle (in air) for light to be guided by total internal reflection? (NA = √(n₁² − n₂²) = sin of the acceptance angle)
Q16. In a compound microscope the objective has focal length 1.0 cm and the object is placed 1.1 cm from it. The eyepiece has focal length 5.0 cm and forms the final image at the near point (25 cm). What is the total magnifying power in magnitude?
Q17. What is the minimum length of a vertical plane mirror in which a person 1.8 m tall can see her entire image?
Q18. A gas goes through the cycle A → B → C → A on a P–V diagram: A (2.0 L, 100 kPa) to B (2.0 L, 300 kPa) at constant volume; B to C (6.0 L, 100 kPa) along a straight line; then C back to A at constant pressure. The cycle is traversed clockwise. What is the net work done by the gas per cycle?
Q19. A diatomic ideal gas (rotational but no vibrational motion contributing) is heated at constant pressure. What percentage of the heat supplied is converted into work of expansion?
Q20. A cup of tea cools from 80 °C to 60 °C in the first 5 minutes in a room at 20 °C. Assuming Newton's law of cooling holds exactly, what is its temperature after a further 5 minutes?
Q21. A solid and its liquid are heated by a heater of constant power. The temperature rises at 2.0 K s⁻¹ in the solid phase and at 1.0 K s⁻¹ in the liquid phase (same mass, no heat losses). What is the ratio of specific heat capacity of the solid to that of the liquid?
Q22. A bimetallic strip is made of brass (α = 19 × 10⁻⁶ K⁻¹) bonded to steel (α = 12 × 10⁻⁶ K⁻¹). When it is heated uniformly, which side lies on the outside (convex side) of the curve?
Q23. One mole of a monatomic ideal gas is mixed with one mole of a diatomic ideal gas (rotation only). What is γ = Cp/Cv for the mixture?
Q24. 1000 J of heat flows by conduction from a reservoir at 500 K to one at 250 K. What is the net change in entropy of the two reservoirs?
Q25. A reversible engine works between a source at 450 K and a sink at 300 K and absorbs 900 J of heat from the source in each cycle. How much work does it deliver per cycle?
Q26. A diatomic ideal gas (γ = 1.4) undergoes an isothermal and an adiabatic change starting from the same point on a P–V diagram. How do the slopes of the two curves compare at that point?
Q27. 50 g of steam at 100 °C is passed into 500 g of water at 20 °C in an insulated container. Taking the latent heat of vaporisation as 2260 J g⁻¹ and the specific heat of water as 4.18 J g⁻¹ K⁻¹, what is the final temperature?
Q28. At what temperature is the average translational kinetic energy of a gas molecule equal to 1.0 eV? (k_B = 1.38 × 10⁻²³ J K⁻¹, 1 eV = 1.60 × 10⁻¹⁹ J)
Q29. A Carnot engine works between a source at 500 K and a sink at 300 K, giving an efficiency of 40%. If both temperatures are lowered by 50 K, what is the new efficiency?
Q30. A hot furnace at 2000 K emits thermal radiation whose intensity peaks at 1450 nm. If its temperature is raised to 3000 K, at what wavelength will the peak be?