ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 2): 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 5 kg crate slides 4 m across a floor where the coefficient of kinetic friction is 0.2. How much work does friction do on the crate? (g = 10 m/s²)
Answer: B. −40 J
Explanation: f = μmg = 0.2 × 50 = 10 N, opposite to the motion: W = −10 × 4 = −40 J.
Q2. How much work is needed to stretch a spring of spring constant 200 N/m by 0.1 m from its natural length?
Answer: C. 1 J
Explanation: W = ½kx² = ½ × 200 × 0.01 = 1 J.
Q3. A spring of spring constant 200 N/m is already stretched by 0.1 m. How much additional work is needed to stretch it to 0.2 m?
Answer: C. 3 J
Explanation: W = ½k(x₂² − x₁²) = ½ × 200 × (0.04 − 0.01) = 3 J.
Q4. A tractor pulls a trailer with a constant force of 500 N at a steady 15 m/s. What power does it supply to the trailer?
Answer: B. 7.5 kW
Explanation: P = Fv = 500 × 15 = 7500 W = 7.5 kW.
Q5. A 2 kW electric pump lifts 600 kg of water through a height of 10 m in one minute. What is its efficiency? (g = 10 m/s²)
Answer: B. 50%
Explanation: Useful power = mgh/t = 600 × 10 × 10/60 = 1000 W; efficiency = 1000/2000 = 50%.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. One kilowatt-hour is equal to:
Q7. The absolute gravitational potential energy of a mass m at distance r from the centre of the Earth (mass M) is −GMm/r. It is negative because:
Q8. Taking g = 10 m/s² and the radius of the Earth R = 6.4 × 10⁶ m, what is the escape velocity from the Earth's surface?
Q9. A ball is thrown vertically upward at 20 m/s. At what height is its speed reduced to half the initial value? (g = 10 m/s²)
Q10. A 2 kg block is released from rest at the top of a rough incline 5 m high and reaches the bottom at 8 m/s. How much energy is dissipated by friction? (g = 10 m/s²)
Q11. For a simple pendulum swinging without air resistance, the potential energy of the bob is greatest:
Q12. A turntable rotates at 90 revolutions per minute. What is its angular speed?
Q13. A point on a wheel is 0.5 m from the axle, and the wheel turns at 4 rad/s. What is the centripetal acceleration of the point?
Q14. A wheel spinning at 20 rad/s is brought uniformly to rest in 10 s. Approximately how many revolutions does it make while stopping?
Q15. A 0.2 kg stone is whirled in a vertical circle of radius 0.5 m on a string. At the lowest point its speed is 5 m/s. What is the tension in the string there? (g = 10 m/s²)
Q16. What is the minimum speed a small body must have at the lowest point of a vertical circle of radius 2 m (on a string) to just complete the loop? (g = 10 m/s²)
Q17. A road curve of radius 90 m is banked at 45°. At what speed can a car take the curve without needing any friction? (g = 10 m/s²)
Q18. A 1000 kg car passes over the top of a hump-backed bridge of radius 40 m at 10 m/s. What normal force does the road exert on the car there? (g = 10 m/s²)
Q19. Two small 1 kg balls are fixed to the ends of a light rod 2 m long. What is the moment of inertia of the system about an axis through the middle of the rod, perpendicular to it?
Q20. A body with moment of inertia 0.2 kg m² rotates at 10 rad/s. What is its angular momentum?
Q21. A uniform solid sphere (I = ⅖MR²) rolls without slipping. What fraction of its total kinetic energy is rotational?
Q22. A 4 kg solid cylindrical garden roller is pushed along the ground at 2 m/s, rolling without slipping. What is its total kinetic energy?
Q23. A flywheel of moment of inertia 4 kg m² spins at 10 rad/s. How much rotational kinetic energy does it store?
Q24. What constant torque is needed to bring a uniform solid disc of mass 2 kg and radius 0.5 m from rest to 20 rad/s in 4 s?
Q25. If the orbital radius of a satellite is increased to four times its original value, its period of revolution becomes:
Q26. Approximately how far from the centre of the Earth does a geostationary satellite orbit?
Q27. According to Einstein's general theory of relativity, gravity is:
Q28. A diver tucks in her body during a dive, reducing her moment of inertia to one-third. What happens to her rotational kinetic energy?
Q29. A car with wheels of radius 0.3 m moves at 18 m/s without skidding. What is the angular speed of its wheels?
Q30. How much work does the centripetal force do on a body in uniform circular motion during one complete revolution?