ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 3): 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 50 N force pulls a box 10 m along the floor with the rope at 60° above the horizontal. The work done by the force is
Answer: D. 250 J
Explanation: W = Fd cosθ = 50 × 10 × 0.5 = 250 J.
Q2. A 2 kg body is lifted at constant speed through 5 m. The work done by gravity on the body is (g = 10 m/s²)
Answer: D. −100 J
Explanation: Gravity acts downward while displacement is upward: W = −mgh = −100 J.
Q3. A spring of constant 200 N/m is stretched from 0.1 m to 0.3 m. The work done in stretching it is
Answer: C. 8 J
Explanation: W = ½k(x₂² − x₁²) = 100(0.09 − 0.01) = 8 J.
Q4. A pendulum bob is released from a height 1.8 m above its lowest point. Its speed at the lowest point is
Answer: D. 6 m/s
Explanation: v = √(2gh) = √(2 × 10 × 1.8) = 6 m/s.
Q5. A machine does 6000 J of work in 20 s. Its power output is
Answer: C. 300 W
Explanation: P = W/t = 6000/20 = 300 W.
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Q6. A car’s engine delivers 20 kW and the car moves at a steady 10 m/s against resistance. The resistive force is
Q7. A body of mass 2 kg moving at 3 m/s is slowed to 1 m/s. The work done on it by the net force is
Q8. A 1 kg ball is dropped from 20 m and rebounds to 5 m. The fraction of its mechanical energy lost in the bounce is
Q9. A motor supplies 250 W of electrical power and lifts a load, doing useful work at the rate of 200 W. Its efficiency is
Q10. A wheel turns at 300 revolutions per minute. Its angular velocity is
Q11. A point on a turntable 0.2 m from the axis moves with ω = 10π rad/s (= 5 rev/s). Its centripetal acceleration is
Q12. A 0.5 kg stone is whirled in a horizontal circle of radius 0.8 m at 4 m/s. The tension in the string is
Q13. If the speed of a body moving in a circle is doubled while the radius stays the same, the centripetal force becomes
Q14. A road bend of radius 40 m is banked at 45°. The speed at which a car needs no friction to take the bend is
Q15. A bucket of water is swung in a vertical circle of radius 0.9 m. The minimum speed at the top for the water to stay in is
Q16. For the same bucket (r = 0.9 m), the minimum speed at the bottom needed to complete the vertical circle is
Q17. A solid disc of mass 4 kg and radius 0.3 m rotates about its central axis. Its moment of inertia is
Q18. A flywheel of moment of inertia 2 kg m² rotates at 10 rad/s. Its rotational kinetic energy is
Q19. A tangential force of 10 N acts at the rim of a wheel of radius 0.5 m and moment of inertia 2.5 kg m². Its angular acceleration is
Q20. A turntable of moment of inertia 200 kg m² spins freely at 2 rad/s. A 50 kg child, initially at rest, steps onto its rim at radius 2 m. The new angular velocity is
Q21. A solid sphere rolls without slipping. The fraction of its total kinetic energy that is rotational is
Q22. A body moves at constant speed in a horizontal circle. The work done by the centripetal force in one complete revolution is
Q23. Taking g = 10 m/s² and Earth’s radius as 6.4 × 10⁶ m, the escape speed from Earth is about
Q24. With the same data, the orbital speed of a satellite just above Earth’s surface is
Q25. If a satellite’s orbital radius is quadrupled, its orbital period becomes
Q26. If a planet had the same mass as Earth but twice Earth’s radius, the acceleration due to gravity at its surface would be
Q27. The geostationary orbit of a satellite lies
Q28. An astronaut in a freely orbiting satellite feels weightless because
Q29. A ball is thrown upward at 20 m/s. At the height where its kinetic energy equals its potential energy (measured from the launch point), the height is
Q30. A 1000 kg car travelling at 72 km/h has kinetic energy