ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Motion, Force and Momentum (Set 4): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer review.…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A car moving at 20 m/s is brought to rest with a uniform deceleration of 4 m/s². The distance it covers in the last 2 s of its motion is
Answer: A. 8 m
Explanation: Reverse the motion: starting from rest with a = 4 m/s², the distance in 2 s is ½(4)(2²) = 8 m.
Q2. A ball is thrown vertically upward at 20 m/s from the top of a 25 m tower. Taking g = 10 m/s², the speed with which it strikes the ground at the foot of the tower is
Answer: B. 30 m/s
Explanation: On returning to the top the speed is 20 m/s downward; then v² = 20² + 2(10)(25) = 900, so v = 30 m/s.
Q3. A stone A is dropped from rest from a tall tower. One second later a stone B is thrown vertically downward at 20 m/s from the same point. B overtakes A at a time, measured from the release of A, of
Answer: D. 1.5 s
Explanation: Equal distances: 5t² = 20(t − 1) + 5(t − 1)². This reduces to 0 = 10t − 15, so t = 1.5 s.
Q4. A projectile has a horizontal range equal to 3 times its maximum height. The tangent of its angle of projection is
Answer: D. 4/3
Explanation: R = 2u²sinθcosθ/g and H = u²sin²θ/2g, so R/H = 4/tanθ = 3, giving tanθ = 4/3.
Q5. A ball is projected horizontally at 40 m/s from the top of a cliff 45 m high. The speed with which it reaches the ground is
Answer: C. 50 m/s
Explanation: vy² = 2gh = 900, so vy = 30 m/s. Speed = √(40² + 30²) = 50 m/s.
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Q6. Two projectiles are launched with the same speed at angles of 30° and 60° to the horizontal. The ratio of their times of flight (30° : 60°) is
Q7. A boat with speed 5 m/s in still water is to cross a river 200 m wide flowing at 3 m/s and land at the point directly opposite its starting point. The time taken is
Q8. A man walking steadily through vertical rain finds the rain appears to fall at 45° to the vertical. If he doubles his walking speed, the tangent of the angle the apparent rain makes with the vertical becomes
Q9. A 5 kg block rests on a smooth plane inclined at θ with tanθ = 3/4. What horizontal force applied to the block keeps it at rest? (g = 10 m/s²)
Q10. A man of mass 60 kg stands on a weighing machine in a lift that is moving upward but slowing down at 2 m/s². The machine reads (in force units, g = 10 m/s²)
Q11. A 4 kg block on a rough horizontal table (μ = 0.25) is joined by a light string over a smooth pulley to a 6 kg block hanging freely. The tension in the string is
Q12. Blocks of 2 kg, 3 kg and 5 kg are in contact in that order on a smooth horizontal surface. A horizontal force of 20 N pushes on the 2 kg block. The contact force between the 3 kg and 5 kg blocks is
Q13. A gun of mass 4 kg fires a bullet of mass 20 g. The ratio of the kinetic energy of the bullet to that of the gun, just after firing, is
Q14. A 2 kg ball moving at 6 m/s strikes a stationary 4 kg ball and the two stick together. The kinetic energy lost in the collision is
Q15. A 1 kg body strikes a stationary 3 kg body head-on in a perfectly elastic collision. The percentage of its kinetic energy transferred to the 3 kg body is
Q16. A 0.5 kg ball hits a smooth wall at 12 m/s with its velocity at 60° to the normal to the wall, and rebounds elastically. The impulse delivered to the wall is
Q17. A force rises uniformly from 0 to 40 N over 0.1 s and then drops abruptly to zero. It acts on a 0.5 kg body initially at rest. The final speed of the body is
Q18. A machine gun fires 20 bullets each second, each of mass 25 g, at a muzzle speed of 600 m/s. The average force on the gun is
Q19. A rocket of initial mass 5000 kg ejects gas at 2000 m/s at a rate of 50 kg/s and lifts off vertically. Its initial acceleration is (g = 10 m/s²)
Q20. A body's speed increases uniformly from 0 to 10 m/s in 5 s, stays constant for 10 s, and then falls uniformly to zero in 5 s. Its average speed over the whole 20 s is
Q21. A particle moves along a line with position x = 3t² − t³ (SI units). The total distance it travels in the first 3 s is
Q22. A book rests on a table. The reaction partner (Newton's third law) of the Earth's gravitational pull on the book is
Q23. Two bodies of masses in the ratio 4 : 9 have equal kinetic energies. The ratio of their linear momenta is
Q24. A block just slides down a rough incline of 37° with constant speed (sin37° = 0.6, cos37° = 0.8). If the incline is raised to 53° (sin53° = 0.8, cos53° = 0.6), its acceleration will be (g = 10 m/s²)
Q25. A 10 kg block lies on a rough floor (μ = 0.5). It is pulled by a rope at 53° above the horizontal (cos53° = 0.6, sin53° = 0.8). The minimum pull needed to just start it moving is
Q26. A ball is thrown vertically upward at 30 m/s. The time interval between its two passes through the point 25 m above the launch point is (g = 10 m/s²)
Q27. A body is dropped from a height. The ratio of the time taken to fall the second half of the height to the time taken to fall the first half is
Q28. A car travels the first half of a journey (by distance) at 30 km/h and the second half at 60 km/h. The average speed for the whole journey is
Q29. A man of mass 50 kg walks 6 m along the length of a 100 kg boat floating on still water (negligible water resistance). The boat moves, relative to the water, through
Q30. A force F = 6t newtons acts on a 2 kg body initially at rest. Its speed after 4 s is