ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 4): 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 variable force F = (3x² + 2x) N acts on a body along the x-axis. The work done in moving it from x = 1 m to x = 3 m is
Answer: A. 34 J
Explanation: W = ∫(3x² + 2x)dx = [x³ + x²] from 1 to 3 = (27 + 9) − (1 + 1) = 34 J.
Q2. A pump lifts 600 kg of water per minute from a well 20 m deep and has an efficiency of 50%. The power supplied to the pump is (g = 10 m/s²)
Answer: A. 4 kW
Explanation: Output power = mgh/t = 600 × 10 × 20/60 = 2000 W. Input = output/efficiency = 2000/0.5 = 4000 W.
Q3. A 1000 kg car has an engine delivering a constant 40 kW. At a steady 20 m/s the resistive force is constant. When its speed is 10 m/s, with the same power and resistive force, its acceleration is
Answer: C. 2 m/s²
Explanation: At steady speed the resistance = P/v = 40000/20 = 2000 N. At 10 m/s the driving force is 4000 N, so a = (4000 − 2000)/1000 = 2 m/s².
Q4. A 2 kg block is released from rest at the top of a rough curved track 5 m high and reaches the bottom at 8 m/s. The work done against friction is (g = 10 m/s²)
Answer: A. 36 J
Explanation: Loss = mgh − ½mv² = 100 − 64 = 36 J.
Q5. The work done in stretching a spring from an extension of 2 cm to 4 cm is how many times the work done in stretching it from its natural length to 2 cm?
Answer: A. 3
Explanation: W ∝ x²: work from 0 to 2 cm ∝ 4, from 2 cm to 4 cm ∝ 16 − 4 = 12. Ratio = 3.
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Q6. A 0.2 kg stone is whirled in a vertical circle of radius 0.5 m. Its speed at the top is 5 m/s. The tension in the string at the bottom is (g = 10 m/s²)
Q7. A track curve of radius 40 m is to be banked so that vehicles can take it at 20 m/s without relying on friction. The angle of banking should be (g = 10 m/s²)
Q8. A car takes a flat circular bend of radius 25 m. If the coefficient of friction is 0.4, the greatest speed at which it can take the bend without skidding is (g = 10 m/s²)
Q9. Four particles of mass 0.5 kg each are at the corners of a square of side 0.4 m, joined by light rods. The moment of inertia about an axis through one corner perpendicular to the plane of the square is
Q10. A solid sphere rolls without slipping on a horizontal surface. The fraction of its total kinetic energy that is rotational is
Q11. A solid disc rolls without slipping down an incline from a vertical height of 2.7 m, starting from rest. Its speed at the bottom is (g = 10 m/s²)
Q12. A flywheel of moment of inertia 0.5 kg m² is acted on by a constant 2.5 N m applied torque against a constant frictional torque of 0.5 N m for 10 s from rest. The applied torque is then removed. The time taken afterwards for the flywheel to stop is
Q13. A uniform horizontal disc of mass 100 kg and radius 2 m rotates at 2 rad/s about a vertical axis. A 25 kg child, initially at rest on the ground, steps onto its rim. The angular speed of the disc becomes
Q14. A wheel starts from rest with a constant angular acceleration of π rad/s². The number of complete revolutions it makes in the first 4 s is
Q15. A wheel of radius 0.5 m rotates at 120 revolutions per minute. The centripetal acceleration of a point on its rim is
Q16. A 500 kg satellite moves in a circular orbit just above the Earth's surface (take radius R = 6400 km, g = 10 m/s²). The minimum additional energy needed to make it escape is
Q17. A satellite is moved from one circular orbit to another of 4 times the radius. Its kinetic energy becomes
Q18. At what height above the Earth's surface is the acceleration due to gravity 36% less than its surface value? (R = 6400 km)
Q19. The angular speed of a geostationary satellite about the Earth's axis is about
Q20. An astronaut in a circular orbit 400 km above the Earth feels weightless mainly because
Q21. A 5 kg box is pushed from rest up a smooth incline of length 5 m and inclination 30° by a force of 100 N parallel to the incline. Its kinetic energy at the top is (g = 10 m/s²)
Q22. A bullet moving at speed v penetrates 9 cm into a fixed wooden block before stopping. The same bullet moving at v/3 would penetrate (assume a constant resistive force)
Q23. A particle has potential energy U = x³ − 6x joules (x in metres). The force on it at x = 2 m is
Q24. A motor drawing 1.5 kW of electrical power raises a 90 kg load at a steady 1 m/s. Its efficiency is (g = 10 m/s²)
Q25. A 3 kW heater runs for 20 minutes. The energy it uses, in megajoules, is
Q26. A 0.2 kg stone is whirled in a horizontal circle of radius 0.5 m on a string that can bear a maximum tension of 40 N. The maximum angular speed is (ignore the string's sag)
Q27. A conical pendulum bob of mass 0.4 kg hangs from a string making an angle θ with the vertical, with cosθ = 0.8. The tension in the string is (g = 10 m/s²)
Q28. A 0.5 kg pendulum bob on a light string is released from the horizontal position. The tension in the string as the bob passes the lowest point is (g = 10 m/s²)
Q29. A uniform disc of mass 4 kg and radius 0.5 m rotates about its axis at 10 rad/s. Its rotational kinetic energy is
Q30. A uniform chain of mass 4 kg and length 2 m lies on a smooth table with half of its length hanging over the edge. The work needed to pull the hanging half back onto the table is (g = 10 m/s²)