NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Mechanics: Motion, Force, Work and Energy (Set 4): 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 swimmer who can swim at 2.0 m s⁻¹ in still water heads straight across a river 100 m wide, in which the current flows at 1.5 m s⁻¹. How far downstream is she carried when she reaches the other bank?
Answer: A. 75 m
Explanation: Crossing time = 100/2.0 = 50 s (only her cross-stream speed matters). Drift = 1.5 × 50 = 75 m.
Q2. A body starts with a speed of 2 m s⁻¹ and accelerates uniformly at 4 m s⁻². How far does it travel during the 5th second of its motion (between t = 4 s and t = 5 s)?
Answer: C. 20 m
Explanation: sₙ = u + a(n − ½) = 2 + 4 × 4.5 = 20 m. Check: s(5) − s(4) = 60 − 40 = 20 m.
Q3. A ball is thrown vertically upward at 20 m s⁻¹ (g = 10 m s⁻²). What total distance does it travel in the first 3 s?
Answer: D. 25 m
Explanation: It rises to 20 m (taking 2 s), then falls for 1 s through ½ × 10 × 1² = 5 m. Total path = 25 m; the displacement is only 15 m.
Q4. For a projectile launched from level ground, at what angle of projection is the maximum height equal to the horizontal range?
Answer: A. 76°
Explanation: H/R = tan θ/4. Setting H = R gives tan θ = 4, θ = 76.0° ≈ 76°.
Q5. A ball rolls off a horizontal table 1.25 m high with a speed of 4 m s⁻¹ (g = 10 m s⁻²). What is its speed just before it hits the floor?
Answer: B. 6.4 m s⁻¹
Explanation: Vertical speed vᵧ = √(2gH) = 5 m s⁻¹; horizontal speed stays 4 m s⁻¹. Speed = √(16 + 25) = √41 = 6.4 m s⁻¹. (Landing 2.0 m from the table.)
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. Masses of 3 kg and 5 kg hang from the ends of a light string passing over a smooth light pulley (g = 10 m s⁻²). What is the tension in the string?
Q7. A block on a rough plank just begins to slide when the plank is slowly tilted to 30° above the horizontal. What is the coefficient of static friction between block and plank?
Q8. A road bend of radius 100 m is to be banked so that vehicles can take it at 20 m s⁻¹ with no reliance on friction (g = 10 m s⁻²). What is the banking angle?
Q9. A conical pendulum has a 1.0 m string making 60° with the vertical (g = 10 m s⁻²). What is the period of one revolution of the bob?
Q10. A uniform chain of mass 4 kg and length 2 m hangs vertically from a hook. How much work is needed to lift it until it lies entirely at the level of the hook (g = 10 m s⁻²)?
Q11. A car of engine power 60 kW is opposed by a total resistive force of 1500 N at high speed. What is its maximum steady speed?
Q12. Two springs of constants 300 N m⁻¹ and 600 N m⁻¹ are joined end to end (in series) and stretched by a total of 5.0 cm. How much elastic energy is stored?
Q13. A 10 g bullet embeds in a 0.99 kg wooden block hanging from strings, and the block rises 0.20 m (g = 10 m s⁻²). What was the speed of the bullet?
Q14. A stationary 6 kg shell explodes into two fragments of 4 kg and 2 kg. The 4 kg fragment moves east at 3 m s⁻¹, and the 2 kg fragment moves west at 6 m s⁻¹. How much kinetic energy is released?
Q15. A ball dropped from a height of 1.00 m onto a hard floor rebounds to 0.64 m. What is the coefficient of restitution?
Q16. Particles of mass 2 kg and 3 kg lie 5.0 m apart on a line. How far is their centre of mass from the 2 kg particle?
Q17. A solid sphere rolls without slipping from rest down an incline, dropping through a height of 0.70 m (g = 10 m s⁻²). What is its speed at the bottom?
Q18. A skater spinning at 2.0 rad s⁻¹ with moment of inertia 4.0 kg m² pulls her arms in, reducing it to 1.6 kg m². How much does her rotational kinetic energy increase?
Q19. A uniform ladder 5 m long weighing 100 N rests with its top on a smooth vertical wall 4 m above the ground and its foot on rough ground (base 3 m from the wall). What horizontal friction force acts at the foot?
Q20. A planet has 8 times the mass of Earth and twice its radius. If the escape speed from Earth is 11.2 km s⁻¹, what is the escape speed from this planet?
Q21. A 200 kg satellite moves in a circular orbit of radius 2R about Earth (R = 6.4 × 10⁶ m, g = 10 m s⁻² at the surface). What is its total mechanical energy?
Q22. A satellite in a low circular orbit slowly loses energy due to thin atmospheric drag. What happens to its orbital radius and its speed?
Q23. A tank 4.0 m high is full of water and has a small hole 2.0 m above the ground (g = 10 m s⁻²). At what horizontal distance from the tank does the jet hit the ground?
Q24. A wooden block of density 600 kg m⁻³ floats in water with 60% of its volume submerged. What fraction is submerged when it floats in oil of density 800 kg m⁻³?
Q25. A metal object of density 7800 kg m⁻³ weighs 78 N in air. What is its apparent weight when completely submerged in water (density 1000 kg m⁻³)?
Q26. Two identical-density spheres fall through the same viscous liquid at terminal velocity. If the radius of one sphere is twice that of the other, what is the ratio of their terminal speeds, large : small?
Q27. What are the dimensions of the coefficient of viscosity η, defined by F = ηA(dv/dx)?
Q28. The mass of a block is measured as 50 ± 0.5 g and its volume as 10 ± 0.2 cm³. What is the density with its maximum uncertainty?
Q29. A vernier caliper has 10 vernier divisions equal to 9 main-scale divisions (1 main division = 1 mm). The zero of the vernier lies just past the 23 mm mark and the 6th vernier line coincides with a main-scale line. What is the reading?
Q30. What is the moment of inertia of a thin ring of mass M and radius R about an axis lying in the plane of the ring and touching it at a point (a tangent in its plane)?