ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 6): 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 spring of force constant 200 N/m is stretched from an extension of 0.10 m to an extension of 0.30 m. The work done on the spring is
Answer: B. 8 J
Explanation: W = ½k(x₂² − x₁²) = 100(0.09 − 0.01) = 8 J.
Q2. A 1000 kg car climbs a road rising 1 m for every 20 m travelled (take sinθ = 1/20) at a steady 10 m/s against a constant 500 N resistance. Take g = 10 m/s². The engine power developed is
Answer: A. 10 kW
Explanation: Driving force = mg sinθ + 500 = 500 + 500 = 1000 N; P = Fv = 1000×10 W = 10 kW.
Q3. A conical pendulum bob moves in a horizontal circle of radius 0.6 m with the string making an angle θ to the vertical, where tan θ = 0.75. Take g = 10 m/s². Its angular speed is
Answer: D. 3.54 rad/s
Explanation: tanθ = ω²r/g, so ω² = 10×0.75/0.6 = 12.5 and ω = 3.54 rad/s.
Q4. A thin uniform spherical shell of mass 3 kg and radius 0.30 m (I = ⅔MR² about a diameter) is made to rotate about a tangent to its surface. Its moment of inertia about this tangent is
Answer: C. 0.45 kg m²
Explanation: I = ⅔MR² + MR² = (5/3)(3)(0.09) = 0.45 kg m².
Q5. A thin hollow spherical shell (I = ⅔MR²) rolls without slipping from rest down an incline, falling through a vertical height of 3 m. Take g = 10 m/s². Its speed at the bottom is
Answer: C. 6 m/s
Explanation: mgh = ½mv²(1 + ⅔) gives v² = 6gh/5 = 36, so v = 6 m/s.
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Q6. A skater spinning at 4 rad/s with moment of inertia 3 kg m² pulls in her arms so that her moment of inertia becomes 1 kg m². The work done by her in pulling in her arms is
Q7. A pulley of moment of inertia 0.5 kg m² and radius 0.2 m has a light string wound round it with a 2 kg mass hanging from the free end. The mass is released and the string does not slip. Taking g = 10 m/s², the acceleration of the mass is
Q8. A 2 kg block slides on a rough horizontal floor with initial speed 10 m/s. The coefficient of kinetic friction is 0.4. Taking g = 10 m/s², the distance it slides before stopping is
Q9. A pump lifts 20 kg of water every second from a well through 25 m and discharges it at 4 m/s. If the pump is 80% efficient, the input power needed is (g = 10 m/s²)
Q10. A 100 kg satellite moves in a circular orbit of radius 2R about the Earth (R = 6.4×10⁶ m, surface g = 10 m/s²). The minimum energy needed to move it to a circular orbit of radius 4R is
Q11. A planet has half the radius of the Earth and one-eighth of its mass. If the escape speed from the Earth is 11.2 km/s, the escape speed from the planet is
Q12. The acceleration due to gravity at the Earth's surface is 10 m/s². At a height equal to the Earth's radius above the surface it is
Q13. A 7 kg body initially at rest is acted on by a force along its path that rises linearly from 0 to 20 N over the first 2 m, stays at 20 N from 2 m to 6 m, then falls linearly to zero by 8 m. Its speed at 8 m (no friction) is
Q14. A 60 N load hangs from two light springs of constants 300 N/m and 600 N/m connected end to end (in series). The elastic energy stored in the combination is
Q15. A flywheel starts from rest and speeds up uniformly to 300 rpm in 10 s. The number of revolutions it makes in this time is
Q16. A car travels at 54 km/h on wheels of radius 0.30 m without slipping. The angular speed of each wheel about its axle is
Q17. A 0.5 kg ball on a light string moves in a vertical circle. The difference between the string tension at the lowest point and at the highest point is
Q18. As a planet moves along its elliptical orbit around the Sun, which of the following remains constant?
Q19. A 0.5 kg bob on a 2 m string is released from rest with the string at 60° to the vertical. The tension in the string as the bob passes the lowest point is (g = 10 m/s²)
Q20. A cyclist rounds a bend of radius 20 m at 10 m/s on level ground. The tangent of the angle his body makes with the vertical, tan θ = v²/(rg), is
Q21. A uniform solid sphere rolls without slipping on a horizontal surface. What fraction of its total kinetic energy is rotational?
Q22. A uniform rod of mass 3 kg and length 1 m carries a 1 kg point mass at each end. The moment of inertia of this system about a perpendicular axis through the rod's centre is
Q23. A uniform disc of mass 4 kg and radius 0.5 m rotates about an axis perpendicular to its plane through a point on its rim. Its moment of inertia about this axis is
Q24. A 2 kg block is dropped from rest from 1.2 m above the top of a vertical spring (k = 200 N/m) fixed on the floor. Taking g = 10 m/s² and ignoring losses, the maximum compression of the spring is
Q25. A constant force of 6 N acts on a 2 kg body initially at rest. The average power delivered in the first 4 s is
Q26. The kinetic energy of a moving body (constant mass) is increased by 44%. By what percentage does its momentum increase?
Q27. A 4 kg object is raised from the Earth's surface to a height equal to the Earth's radius R = 6.4×10⁶ m. Taking surface g = 10 m/s², the gain in its gravitational potential energy is
Q28. Water falls 40 m at 500 kg/s onto a turbine-generator set of overall efficiency 75%. Taking g = 10 m/s², the electrical power output is
Q29. An 800 kg car crosses the bottom of a circular dip of radius 50 m at 10 m/s. Take g = 10 m/s². The normal force from the road at the bottom of the dip is
Q30. A 2 kg block slides 5 m down a rough plane inclined at 30° to the horizontal. Taking g = 10 m/s², the work done on it by gravity during the slide is