ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 1): 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 force F = (3i + 4j) N moves a body through a displacement d = (2i + j) m. How much work is done?
Answer: B. 10 J
Explanation: W = F·d = 3 × 2 + 4 × 1 = 10 J.
Q2. A 50 N force acting at 60° to the direction of motion moves a body 10 m. What work does the force do?
Answer: D. 250 J
Explanation: W = Fd cos θ = 50 × 10 × cos 60° = 250 J.
Q3. A 2 kg box is lifted vertically through 5 m. What is the work done by the gravitational force on the box? (g = 10 m/s²)
Answer: C. −100 J
Explanation: Gravity (20 N downward) is opposite to the upward displacement: W = −mgh = −2 × 10 × 5 = −100 J.
Q4. A motor lifts a 100 kg load through a height of 12 m in 20 s at constant speed. What is its power output? (g = 10 m/s²)
Answer: D. 600 W
Explanation: P = mgh/t = 100 × 10 × 12/20 = 600 W.
Q5. A car's engine delivers 30 kW while the car moves at a constant 20 m/s on a level road. What is the total resistive force on the car?
Answer: A. 1500 N
Explanation: At constant speed the driving force equals resistance: F = P/v = 30000/20 = 1500 N.
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Q6. The work done by a variable force over a displacement can be found from a force–displacement graph as:
Q7. The speed of a 3 kg body increases from 2 m/s to 4 m/s. How much net work was done on it?
Q8. A ball is dropped from a height of 20 m. With what speed does it strike the ground? (g = 10 m/s², no air resistance)
Q9. A ball is dropped from a height of 20 m. At what height above the ground are its kinetic and potential energies equal (no air resistance)?
Q10. Near the Earth's surface, the escape velocity is related to the orbital velocity of a close-orbiting satellite by:
Q11. Which statement about a conservative force is correct?
Q12. A pendulum bob is released from rest at a height of 0.8 m above its lowest point. What is its speed at the lowest point? (g = 10 m/s²)
Q13. A ceiling fan completes 300 rotations in one minute. What is its angular speed?
Q14. A grinding disc speeds up from rest at a constant 2 rad/s². What angle does it sweep out during its first 5 s?
Q15. A wheel of radius 0.5 m rotates at 8 rad/s. What is the linear speed of a point on its rim?
Q16. A 0.5 kg stone tied to a string is whirled in a horizontal circle of radius 1 m at 4 m/s. What is the centripetal force?
Q17. A car takes an unbanked curve of radius 20 m. If the coefficient of friction between tyres and road is 0.5, what is the maximum safe speed? (g = 10 m/s²)
Q18. At what angle should a road curve of radius 40 m be banked so that a car can take it at 20 m/s without relying on friction? (g = 10 m/s²)
Q19. A bucket of water is swung in a vertical circle of radius 2.5 m. What is the minimum speed at the top so the water does not fall out? (g = 10 m/s²)
Q20. What is the moment of inertia of a uniform solid disc of mass 2 kg and radius 0.2 m about its central axis perpendicular to its face?
Q21. A uniform solid disc rolls without slipping on a level surface. What fraction of its total kinetic energy is rotational?
Q22. A solid cylinder starts from rest and rolls without slipping down an incline through a vertical height of 1.2 m. What is its speed at the bottom? (g = 10 m/s²)
Q23. A skater spinning at 3 rev/s with moment of inertia 4 kg m² pulls in her arms, reducing her moment of inertia to 2 kg m². What is her new rate of spin?
Q24. A torque of 2 N m acts on a wheel of moment of inertia 0.5 kg m². What angular acceleration does it produce?
Q25. If the orbital radius of a satellite is made four times larger, its orbital speed becomes:
Q26. Taking g = 10 m/s² and Earth's radius R = 6.4 × 10⁶ m, what is the orbital speed of a satellite just above the Earth's surface?
Q27. A space station is a ring of radius 160 m. At what angular speed must it rotate so that astronauts on the rim feel an artificial gravity of 10 m/s²?
Q28. An astronaut in a satellite orbiting the Earth feels weightless because:
Q29. Which statement about a geostationary satellite is correct?
Q30. A 2 kg block sliding at 10 m/s on a horizontal rough surface comes to rest. If the coefficient of kinetic friction is 0.5, how far does it slide? (g = 10 m/s²)