NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Mechanics: Motion, Force, Work and Energy (Set 5): 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 starts from rest and accelerates uniformly at 2.0 m s⁻² for 10 s, then moves at constant speed for the next 20 s. What is its average speed over the whole 30 s?
Answer: A. 16.7 m s⁻¹
Explanation: Stage 1: s = ½ × 2 × 10² = 100 m, final speed 20 m s⁻¹. Stage 2: 20 × 20 = 400 m. Total 500 m in 30 s gives 16.7 m s⁻¹ (not the mean of 0 and 20).
Q2. A driver travelling at 20 m s⁻¹ sees a hazard. The reaction time is 0.50 s, after which the brakes give a constant deceleration of 5.0 m s⁻². What is the total distance travelled from the moment of seeing the hazard until the car stops?
Answer: D. 50 m
Explanation: Reaction distance = 20 × 0.50 = 10 m. Braking distance = v²/2a = 400/10 = 40 m. Total = 50 m.
Q3. Rain falls vertically at 10 m s⁻¹ relative to the ground. A man walks on level ground at 5.0 m s⁻¹. At what angle to the vertical must he hold his umbrella to keep the rain off?
Answer: C. 26.6°, tilted toward the direction he is walking
Explanation: Relative to him the rain has a vertical component 10 m s⁻¹ downward and a horizontal component 5 m s⁻¹ backward, so it comes from the front: tan θ = 5/10, θ = 26.6° from the vertical, and the umbrella is tilted forward.
Q4. A ball is thrown horizontally at 12 m s⁻¹ from the top of a 45 m high cliff. Taking g = 10 m s⁻² and neglecting air resistance, what is its speed just before it hits the ground?
Answer: A. 32.3 m s⁻¹
Explanation: Fall time t = √(2 × 45/10) = 3.0 s, so v_y = 30 m s⁻¹. Speed = √(12² + 30²) = √1044 = 32.3 m s⁻¹.
Q5. At what angle of projection (above the horizontal) are the horizontal range and the maximum height of a projectile numerically equal?
Answer: A. tan⁻¹(4), about 76°
Explanation: R = 2u² sinθ cosθ/g and H = u² sin²θ/2g. R = H gives 2 cosθ = sinθ/2, so tanθ = 4, θ ≈ 76°.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. A block slides down a 30° incline with coefficient of kinetic friction 0.20. Taking g = 10 m s⁻², what is its acceleration?
Q7. Masses of 3.0 kg and 5.0 kg hang from the two ends of a light string passing over a smooth, light pulley (Atwood machine). Taking g = 10 m s⁻², what is the tension in the string?
Q8. A uniform chain of mass 4.0 kg and length 2.0 m lies on a smooth table with half of its length hanging over the edge. How much work is needed to pull the hanging half slowly onto the table? (g = 10 m s⁻²)
Q9. A car engine delivers 60 kW to the wheels. The resistive force is a constant 1500 N. What is the maximum speed the car can sustain on a level road?
Q10. A small block slides without friction from rest down a track and enters a vertical circular loop of radius 4.0 m at its bottom. What is the minimum starting height above the bottom of the loop so that the block just completes the loop? (Treat it as a point mass.)
Q11. A 6.0 kg shell at rest explodes into two fragments of 2.0 kg and 4.0 kg. The 4.0 kg fragment moves at 3.0 m s⁻¹. How much kinetic energy is released in the explosion?
Q12. A flywheel with moment of inertia 5.0 kg m² is acted on by a constant torque of 20 N m starting from rest. What is its rotational kinetic energy after 5.0 s?
Q13. A uniform 6.0 m beam of mass 20 kg rests horizontally on supports at its two ends. A 30 kg load is placed 2.0 m from the left end. Taking g = 10 m s⁻², what is the reaction force at the left support?
Q14. A planet has 1/8 of Earth's mass and half of Earth's radius. A person has weight 600 N on Earth. What would be the weight on this planet? (Use g_planet = GM/R².)
Q15. A 500 kg satellite in a circular orbit just above Earth's surface (r = R = 6.4 × 10⁶ m) is moved to a circular orbit of radius 2R. Using total orbital energy E = −GMm/2r and g = 10 m s⁻² at the surface, how much energy must be supplied?
Q16. According to Poiseuille's law, the volume flow rate of blood through a vessel at a fixed pressure difference is proportional to r⁴ (r = radius), other factors unchanged. If plaque narrows an artery's radius to 80% of its original value, by what factor does the flow fall?
Q17. The aorta of radius 1.0 cm carries blood at 0.30 m s⁻¹. The total cross-sectional area of all the capillaries is 2000 times the cross-sectional area of the aorta. What is the average blood speed in the capillaries?
Q18. Assume the time period T of a simple pendulum depends only on its length l and the acceleration due to gravity g, as T = k lᵃ gᵇ with k dimensionless. What are a and b?
Q19. The density of a solid cylinder is found from ρ = m/(πr²h). The percentage uncertainties in m, r and h are 3%, 1% and 2% respectively. What is the maximum percentage uncertainty in ρ?
Q20. A screw gauge has pitch 0.50 mm and 50 divisions on the circular scale. When the jaws are closed the reading is +2 divisions (positive zero error). In measuring a wire the main scale shows 3.0 mm and the 27th circular division coincides with the reference line. What is the corrected diameter?
Q21. Two vectors have magnitudes 5.0 and 12 units. Which of the following could NOT be the magnitude of their resultant?
Q22. A 0.50 kg ball at rest receives a force that rises uniformly from 0 to 20 N in 0.10 s and then drops to zero instantly (a triangular force–time graph). What is the speed of the ball afterwards?
Q23. A 20 g bullet leaves a 4.0 kg rifle (initially at rest) at 400 m s⁻¹. What is the kinetic energy of the recoiling rifle?
Q24. A car travels on a flat circular road of radius 50 m. The coefficient of static friction between tyres and road is 0.40 and g = 10 m s⁻². What is the greatest speed at which it can take the bend without skidding?
Q25. A cylindrical space station of radius 250 m rotates about its axis so that people on the inner rim experience an apparent gravity of g = 10 m s⁻². What is its rotation period?
Q26. A 2.0 kg block, initially at rest on a rough horizontal surface (μ_k = 0.20, g = 10 m s⁻²), is pushed by a constant horizontal force of 10 N through 5.0 m. What is its final speed?
Q27. Two springs of force constants 100 N m⁻¹ and 300 N m⁻¹ are connected end to end (in series), and the combination is stretched by a 15 N force. What is the total extension?
Q28. Using R = 6.4 × 10⁶ m and g = 9.8 m s⁻², what is the orbital period of a satellite skimming just above Earth's surface (T = 2π√(R/g))?
Q29. A hydraulic lift has a small piston of area 10 cm² and a large piston of area 500 cm². What force on the small piston is needed to balance a load of 5000 N on the large piston? (Ignore the weight of the pistons.)
Q30. Two bodies of masses 1.0 kg and 4.0 kg have the same kinetic energy. What is the ratio of their momenta (lighter : heavier)?