NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Mechanics: Motion, Force, Work and Energy (Set 7): 30 multiple-choice questions (40 minutes) with instant scoring and a full…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A car travelling at 72 km h⁻¹ has a driver whose reaction time is 0.50 s; once the brakes act, the car decelerates uniformly at 5.0 m s⁻². What is the total stopping distance from the moment the driver sees the hazard?
Answer: D. 50 m
Explanation: 72 km/h = 20 m/s. Reaction: 20 × 0.50 = 10 m; braking: v²/2a = 400/10 = 40 m; total = 50 m.
Q2. A ball is thrown at 25 m s⁻¹ at 53° above the horizontal on level ground (take g = 10 m s⁻², sin 53° = 0.8, cos 53° = 0.6; neglect air resistance). What is its horizontal range?
Answer: C. 60 m
Explanation: Range = 2v² sinθ cosθ/g = 2 × 625 × 0.8 × 0.6/10 = 60 m (time of flight 4 s).
Q3. A 4.0 kg block on a smooth horizontal table is joined by a light string over a smooth pulley at the table edge to a 1.0 kg block hanging vertically (g = 10 m s⁻²). What is the tension in the string?
Answer: C. 8.0 N
Explanation: a = m₂g/(m₁ + m₂) = 10/5 = 2.0 m s⁻²; T = m₁a = 4.0 × 2.0 = 8.0 N (less than the 10 N weight of the hanging block).
Q4. A block slides down a rough plane inclined at 37° to the horizontal; the coefficient of kinetic friction is 0.50 (take g = 10 m s⁻², sin 37° = 0.6, cos 37° = 0.8). What is its acceleration down the plane?
Answer: C. 2.0 m s⁻²
Explanation: a = g(sinθ − μ cosθ) = 10(0.6 − 0.5 × 0.8) = 2.0 m s⁻².
Q5. A crate is pulled 5.0 m along a horizontal floor by a rope exerting a constant 60 N force at 60° above the horizontal. How much work does the rope do?
Answer: A. 150 J
Explanation: W = Fd cosθ = 60 × 5.0 × cos 60° = 150 J.
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Q6. A pump raises 600 kg of water every minute through a height of 20 m (g = 10 m s⁻²). If its efficiency is 50%, what input power does it need?
Q7. A 2.0 kg trolley moving at 6.0 m s⁻¹ collides with a stationary 4.0 kg trolley and they stick together. What fraction of the initial kinetic energy is lost?
Q8. A thin hoop (all mass at radius R) rolls without slipping from rest down an incline, falling through a vertical height of 0.90 m (g = 10 m s⁻²). What is its speed at the bottom?
Q9. Two 2.0 kg point masses are fixed at the ends of a light rod 1.0 m long. What is the moment of inertia of the system about an axis perpendicular to the rod through one end?
Q10. A skater spinning with arms outstretched pulls them in so that her moment of inertia halves. Ignoring friction, by what factor does her rotational kinetic energy change?
Q11. A planet has twice the mass of the Earth and half its radius. How does its escape velocity compare with the Earth's (11.2 km s⁻¹)?
Q12. Satellite A orbits a planet at a radius four times that of satellite B. What is the ratio of their orbital periods, T(A) : T(B)?
Q13. A comet's distance from the Sun at perihelion is one-third of its distance at aphelion. What is the ratio of its speed at perihelion to that at aphelion?
Q14. A uniform block of density 600 kg m⁻³ floats in oil of density 800 kg m⁻³. What fraction of its volume is submerged?
Q15. Water flows at 2.0 m s⁻¹ through a horizontal pipe of diameter 10 cm which narrows to a diameter of 5 cm. By how much does the pressure drop in the narrow section? (ρ = 1000 kg m⁻³)
Q16. A tall tank stands on the ground with a small hole in its side 3.2 m above the ground. Water is 1.8 m deep above that hole. At what horizontal distance from the tank does the jet hit the ground? (Neglect air resistance; Torricelli's theorem applies; g = 10 m s⁻²)
Q17. The radius of a spherical ball falling through a viscous liquid is doubled, with the densities of ball and liquid unchanged. By what factor does its terminal speed change?
Q18. Soap solution has a surface tension of 0.030 N m⁻¹. What is the excess pressure inside a soap bubble (two surfaces) of radius 1.0 cm?
Q19. A wire of length 2.0 m and cross-section 1.0 mm² stretches by 1.0 mm under a load of 100 N. How much elastic potential energy is stored in the wire?
Q20. For A = i + 2j + 3k and B = 2i + j, what is the vector product A × B?
Q21. What are the SI dimensions of the coefficient of viscosity η?
Q22. The acceleration due to gravity is found from a pendulum using g = 4π²L/T². If L is measured with a 1% error and T with a 1% error, what is the maximum percentage error in g?
Q23. Three lengths 12.11 m, 18.0 m and 1.013 m are added. What is the sum expressed to the correct number of significant figures?
Q24. A 0.20 kg stone is whirled in a horizontal circle of radius 0.50 m at 2.0 revolutions per second (take π² = 9.87). What is the tension in the string, ignoring gravity?
Q25. A boat can travel at 5.0 m s⁻¹ in still water and wishes to cross a river 100 m wide, flowing at 3.0 m s⁻¹, so as to land directly opposite its starting point. How long does the crossing take?
Q26. A 0.15 kg ball approaching a bat at 20 m s⁻¹ is hit straight back at 30 m s⁻¹. If the contact lasts 5.0 ms, what is the average force on the ball?
Q27. A force F = (4x + 2) N acts on a body along the x-axis. How much work does it do in moving the body from x = 1.0 m to x = 3.0 m?
Q28. A uniform metre rule of weight 2.0 N is pivoted at the 30 cm mark. What weight hung at the 5 cm mark keeps it horizontal?
Q29. A spring of constant 200 N m⁻¹ is compressed by 0.10 m and used to launch a 0.10 kg ball along a smooth horizontal surface. What is the launch speed?
Q30. A ball is thrown vertically upward at 30 m s⁻¹ from the ground (g = 10 m s⁻²; ignore air resistance). What total distance does it travel in the first 4.0 s?