ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 7): 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. The force on a trolley rises uniformly from 0 to 10 N during the first 2 m of its travel, then stays constant at 10 N for the next 3 m. The total work done by the force is:
Answer: D. 40 J
Explanation: Area under F–x graph: ½(2)(10) + (3)(10) = 10 + 30 = 40 J.
Q2. A pump raises 600 kg of water each minute from a well to a tank 20 m higher and has an efficiency of 80%. Taking g = 10 m/s², the power it draws is:
Answer: C. 2500 W
Explanation: Output power = 600 × 10 × 20/60 = 2000 W; input = 2000/0.8 = 2500 W.
Q3. A 1000 kg car moves at a steady 20 m/s on a level road against a total resistive force of 500 N. The engine power needed is:
Answer: D. 10 kW
Explanation: At constant speed the driving force equals the resistance: P = Fv = 500 × 20 = 10 000 W = 10 kW.
Q4. The net work needed to increase the speed of a 2 kg body from 3 m/s to 5 m/s is:
Answer: B. 16 J
Explanation: W = ½m(v² − u²) = ½(2)(25 − 9) = 16 J.
Q5. A spring of force constant 800 N/m is compressed by 0.1 m. The additional work needed to compress it from 0.1 m to 0.2 m is:
Answer: D. 12 J
Explanation: W = ½k(x₂² − x₁²) = ½(800)(0.04 − 0.01) = 12 J.
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Q6. A small block slides from rest down a smooth curved track and drops through a vertical height of 1.8 m. Taking g = 10 m/s², its speed at the bottom is:
Q7. A block sliding on a horizontal floor at 8 m/s comes to rest after 16 m. Taking g = 10 m/s², the coefficient of kinetic friction is:
Q8. A 0.5 kg ball whirled in a vertical circle of radius 1 m on a light string has speed 5 m/s at the top of the circle. Taking g = 10 m/s², the tension at the top is:
Q9. A frictionless banked curve of radius 40 m has tan θ = 0.25. Taking g = 10 m/s², the speed at which a car needs no friction to round it is:
Q10. A car rounds a curve of radius 50 m at a constant speed of 20 m/s. Its acceleration is:
Q11. A flywheel turns at 120 revolutions per minute. Its angular velocity is:
Q12. A wheel starts from rest with a constant angular acceleration of 2 rad/s². The angle it turns through in the first 5 s is:
Q13. A ring and a uniform disc have the same mass and radius, each rotating about its central axis perpendicular to its plane. The ratio I_ring : I_disc is:
Q14. A solid cylinder rolls without slipping from rest down a ramp, descending a vertical height of 2.7 m. Taking g = 10 m/s², its speed at the bottom is (I = ½MR²):
Q15. A disc of moment of inertia 2 kg m² spins at 6 rad/s about its axis. A second, non-rotating disc of moment of inertia 1 kg m² is dropped coaxially onto it and they move together. The kinetic energy lost is:
Q16. A constant torque of 20 N m acts on a flywheel of moment of inertia 4 kg m², starting from rest. The time it takes to reach 25 rad/s is:
Q17. A thin hoop of mass 2 kg and radius 0.5 m spins about its axis at 10 rad/s. Its rotational kinetic energy is:
Q18. Satellite A orbits a planet at radius r and satellite B at radius 4r. The ratio of their orbital periods T_B/T_A is:
Q19. A planet has 8 times the mass and twice the radius of Earth. If Earth's escape velocity is 11.2 km/s, the escape velocity from this planet is:
Q20. A person weighs 100 N on the surface of Earth (radius R). Treating Earth as a uniform sphere, the person's weight at a height R above the surface is:
Q21. Astronauts inside a spacecraft orbiting Earth with its engines off feel weightless because:
Q22. A geostationary satellite stays above the same point on Earth. This requires that its orbit:
Q23. The work needed to lift a 2 kg object from Earth's surface to a height equal to Earth's radius R = 6.4 × 10⁶ m is (take g = 10 m/s² at the surface):
Q24. A force is called conservative if:
Q25. Two machines are connected in series, so the output of the first is the input of the second. Their efficiencies are 80% and 50%. The overall efficiency is:
Q26. A 60 W lamp is kept on for 5 hours. The energy it uses is:
Q27. A ring-shaped space station of radius 40 m rotates to give a centripetal acceleration of 10 m/s² at its rim. Its angular velocity must be:
Q28. A point on the rim of a wheel of radius 1 m has angular velocity 3 rad/s and angular acceleration 12 rad/s² at some instant. The magnitude of its total linear acceleration is:
Q29. A lawn mower is pushed through 10 m by a 100 N force acting along the handle, which makes 37° with the horizontal ground. Taking cos 37° = 0.8, the work done is:
Q30. A 1 kg ball is thrown at 20 m/s at 60° above the horizontal. Ignoring air resistance, its kinetic energy at the highest point is: