NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Mechanics: Motion, Force, Work and Energy (Set 6): 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. Two trains 100 km apart move towards each other at 40 km/h and 60 km/h on the same track. A bird flies back and forth between their fronts at a constant 80 km/h until the trains meet. What total distance does the bird cover?
Answer: D. 80 km
Explanation: The trains close the gap at 40 + 60 = 100 km/h, so they meet after 1.0 h. The bird flies at 80 km/h for the whole hour, covering 80 km. (No sum of back-and-forth legs is needed.)
Q2. On a velocity–time graph, a car's speed rises uniformly from 0 to 20 m s⁻¹ in 10 s, stays constant for 30 s, and then falls uniformly to rest in 20 s. What is its average velocity over the whole 60 s?
Answer: B. 15 m s⁻¹
Explanation: Displacement = area under the graph = ½(10)(20) + (30)(20) + ½(20)(20) = 100 + 600 + 200 = 900 m. Average velocity = 900/60 = 15 m s⁻¹.
Q3. A stone dropped from rest from the top of a tower falls 45 m in the last second of its flight. Taking g = 10 m s⁻² and neglecting air resistance, what is the height of the tower?
Answer: B. 125 m
Explanation: Distance in the nth second = (g/2)(2n − 1) = 5(2n − 1) = 45, so 2n − 1 = 9 and n = 5 s. H = ½ × 10 × 5² = 125 m.
Q4. A stone is dropped from a bridge. Exactly 1.0 s later a second stone is thrown vertically downward from the same point with an initial speed of 20 m s⁻¹. Taking g = 10 m s⁻², how far below the bridge does the second stone catch up with the first?
Answer: C. 11.25 m
Explanation: Let t be the time since the first was dropped: 5t² = 20(t − 1) + 5(t − 1)². Expanding, 0 = 10t − 15, so t = 1.5 s. Distance = 5 × (1.5)² = 11.25 m.
Q5. A projectile on level ground has a horizontal range exactly equal to its maximum height. What is its angle of projection above the horizontal? (R = u² sin2θ/g, H = u² sin²θ/2g)
Answer: A. 76°
Explanation: R = H gives 2 sinθ cosθ = sin²θ/2, so tanθ = 4 and θ = tan⁻¹ 4 = 76°.
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Q6. A ball is thrown horizontally at 15 m s⁻¹ from the edge of a 20 m high cliff. Taking g = 10 m s⁻² and ignoring air resistance, with what speed does it hit the ground?
Q7. A 2.0 kg block rests on top of an 8.0 kg block, which lies on a frictionless table. The coefficient of static friction between the two blocks is 0.40. A horizontal force F pulls the lower block. Taking g = 10 m s⁻², what is the largest F for which the upper block does not slip?
Q8. A 0.20 kg pendulum bob on a light string is released from rest with the string horizontal. What is the tension in the string when the bob passes through its lowest point? (g = 10 m s⁻²)
Q9. A block is projected up a rough 30° incline with an initial speed of 6.0 m s⁻¹. The coefficient of kinetic friction is 0.35. Taking g = 10 m s⁻², how far up the slope does it travel before stopping?
Q10. A pump lifts 1200 kg of water per minute through a height of 15 m and its overall efficiency is 60%. Taking g = 10 m s⁻², what electrical power must it draw?
Q11. A moving block of mass 1.0 kg collides head-on and elastically with a stationary block of mass 3.0 kg. What fraction of the incident kinetic energy is transferred to the heavier block?
Q12. A 50 kg person standing at one end of a 100 kg boat at rest on still water walks 3.0 m towards the other end, relative to the boat. Ignoring water resistance, how far does the boat move?
Q13. A thin hollow cylinder (a ring, I = MR²) rolls without slipping down a 30° incline. Taking g = 10 m s⁻², what is the acceleration of its centre?
Q14. A 2.0 kg mass hangs from a light string wrapped round a pulley of radius 0.50 m and moment of inertia 0.50 kg m². The mass is released from rest (g = 10 m s⁻², no slipping or friction). What is its downward acceleration?
Q15. A playground roundabout has moment of inertia 200 kg m² and rotates at 2.0 rad s⁻¹. A 25 kg child runs tangentially and jumps on at the rim, 2.0 m from the axis, having no initial angular momentum about the axis. What is the new angular speed?
Q16. Treating Earth as a uniform sphere of radius R, what is the acceleration due to gravity at a depth R/4 below the surface? (g at the surface = 10 m s⁻²)
Q17. A comet's closest approach to the Sun is 1.0 AU and its farthest distance is 1.5 AU. What is the ratio of its speed at closest approach to its speed at farthest distance?
Q18. A soap bubble of radius 2.0 cm is blown from a solution of surface tension 0.030 N m⁻¹. What is the excess pressure inside the bubble over the outside air? (A soap film has two surfaces, ΔP = 4T/r)
Q19. The quantity √(g/l), where g is an acceleration and l is a length, has the same dimensions as which of these?
Q20. The mass of a moving trolley is measured with a 2% error and its speed with a 3% error. What is the maximum percentage error in its calculated kinetic energy, ½mv²?
Q21. What is the magnitude of the vector product of A = 2î + 3ĵ + k̂ and B = î − ĵ + 2k̂ (that is, the area of the parallelogram they span)?
Q22. A block is dragged along a horizontal floor at constant speed by a rope inclined above the horizontal. The coefficient of kinetic friction is 0.75. At what rope angle is the pulling force a minimum?
Q23. A cyclist rounds a flat circular bend of radius 20 m at 10 m s⁻¹, leaning inwards so that the resultant ground force passes through the centre of mass. At what angle to the vertical does she lean? (g = 10 m s⁻²)
Q24. A steel wire 2.0 m long with cross-section 1.0 mm² (Y = 2.0 × 10¹¹ Pa) carries a load of 100 N. How much elastic energy is stored in the wire?
Q25. A spring of force constant 500 N m⁻¹ is compressed by 8.0 cm and used to launch a 0.10 kg ball vertically upward (g = 10 m s⁻²). Neglecting losses, to what height above the release point does the ball rise?
Q26. A horizontal water jet of cross-section 10 cm² strikes a vertical wall at 15 m s⁻¹ and stops without rebounding (density of water 1000 kg m⁻³). What force does the water exert on the wall?
Q27. What fraction of its total kinetic energy is rotational when a solid sphere (I = 2MR²/5) rolls without slipping on a horizontal surface?
Q28. A uniform rod of mass 3.0 kg and length 1.2 m rotates about an axis perpendicular to the rod, passing through a point 0.30 m from one end. What is its moment of inertia about this axis?
Q29. A tank stands on level ground and is filled with water to a depth of 1.0 m. A small hole is made in its side 0.20 m above the ground. At what horizontal distance from the tank does the jet land? (Use v = √(2gh) for the efflux speed; g = 10 m s⁻²)
Q30. A 100 kg satellite moves in a circular orbit at a height equal to Earth's radius above the surface. What is its kinetic energy? (R = 6.4 × 10⁶ m, g at the surface = 10 m s⁻²)