Power and conservation of mechanical energy - Question Bank

1. The work done by friction on a moving object is always:
A) Positive
B) Negative
C) Zero
D) Can be positive or negative
2. A spring is compressed by 0.1 m. If the potential energy stored is 5 J, what is the spring constant?
A) 500 N/m
B) 1000 N/m
C) 250 N/m
D) 50 N/m
3. Which of the following is a scalar quantity?
A) Force
B) Velocity
C) Power
D) Momentum
4. A body of mass 1 kg falls from a height of 10 m. Its kinetic energy just before hitting the ground is (g=10 m/s²):
A) 10 J
B) 100 J
C) 1 J
D) 0.1 J
5. If a force F acts on a particle such that the position vector is r, the instantaneous power is given by:
A) P = F · (dr/dt)
B) P = F · r
C) P = F / (dr/dt)
D) P = F + (dr/dt)
6. A 60 kg person climbs stairs of height 10 m in 20 seconds. The power developed by the person is (g=10 m/s²):
A) 300 W
B) 30 W
C) 3000 W
D) 30000 W
7. When a non-conservative force does work on a system, the total mechanical energy:
A) Remains constant
B) Increases
C) Decreases
D) Becomes zero
8. A spring with spring constant k is stretched by a distance x. The work done to stretch it further by x is:
A) kx²/2
B) kx²
C) 3kx²/2
D) 2kx²
9. Which of the following is a unit of power?
A) Joule-second
B) Newton-meter
C) Watt
D) Kilogram-meter per second
10. A body is projected upwards. Its mechanical energy:
A) Increases
B) Decreases
C) Remains constant (ignoring air resistance)
D) Becomes zero at the highest point
11. If the velocity of a body is halved, its kinetic energy becomes:
A) Half
B) One fourth
C) Double
D) Four times
12. A constant power P is supplied to a particle. The velocity of the particle is proportional to:
A) t
B) t²
C) t^(1/2)
D) t^(-1/2)
13. Which of the following is an example of potential energy?
A) Energy of a moving car
B) Energy stored in a compressed spring
C) Energy of a sound wave
D) Energy dissipated as heat
14. A 2 kg object is moving with a velocity of 3 m/s. If a force of 6 N acts on it in the direction of motion, what is its kinetic energy after 2 seconds?
A) 10.5 J
B) 27 J
C) 40.5 J
D) 57 J
15. If the total mechanical energy of a system is conserved, then the sum of kinetic and potential energy:
A) Increases
B) Decreases
C) Remains constant
D) Is zero
16. A body of mass m is at rest. If it is acted upon by a constant force F for time t, its kinetic energy is proportional to:
A) m
B) F
C) t
D) F²t²
17. What is the power of a person who lifts 20 kg of mass to a height of 5 m in 10 seconds? (g = 10 m/s²)
A) 10 W
B) 100 W
C) 20 W
D) 50 W
18. The potential energy of a system can change due to the work done by:
A) Only conservative forces
B) Only non-conservative forces
C) Both conservative and non-conservative forces
D) No forces
19. In which scenario is mechanical energy conserved?
A) A ball falling through viscous oil
B) A block sliding down a rough inclined plane
C) A planet revolving around the sun
D) A spring oscillating after being stretched and released
20. A 1000 kg car travels at 20 m/s. If the engine develops a power of 50 kW, how much time does it take to cover 1 km?
A) 20 s
B) 40 s
C) 10 s
D) 50 s
21. A force F = (3i - 2j + k) N acts on a particle, and the particle is displaced by d = (4i + 5j + 3k) m. Calculate the work done by the force.
A) 1 J
B) 10 J
C) 22 J
D) 19 J
22. When a spring is stretched or compressed from its equilibrium position, work is done against the spring force, which is stored as:
A) Kinetic energy
B) Heat energy
C) Elastic potential energy
D) Chemical energy
23. A car engine does 5000 J of work in 10 seconds. What is its power output?
A) 500 J/s
B) 50000 W
C) 50 W
D) 500 W
24. A body of mass 5 kg is projected vertically upwards with an initial velocity of 20 m/s. What is its maximum height? (g = 10 m/s²)
A) 10 m
B) 20 m
C) 40 m
D) 50 m
25. Which of the following represents the change in potential energy when a conservative force does work Wc?
A) ΔPE = Wc
B) ΔPE = -Wc
C) ΔPE = 1/Wc
D) ΔPE = -1/Wc
26. If the speed of a body is doubled, its kinetic energy becomes:
A) Half
B) Double
C) Four times
D) Eight times
27. What is the power of a pump that lifts 500 kg of water to a height of 10 m in 1 minute? (g = 10 m/s²)
A) 833.3 W
B) 5000 W
C) 500 W
D) 83.3 W
28. A force F = (2i + 3j) N moves an object through a displacement d = (4i + 2j) m. Calculate the work done.
A) 14 J
B) 20 J
C) 8 J
D) 6 J
29. When work is done against a conservative force, the potential energy of the system:
A) Decreases
B) Increases
C) Remains unchanged
D) Becomes zero
30. A spring is compressed by 5 cm. If the spring constant is 200 N/m, calculate the potential energy stored.
A) 0.25 J
B) 0.5 J
C) 1 J
D) 0.125 J
31. A body of mass m is at rest. If a constant force F acts on it, its kinetic energy after time t will be proportional to:
A) t
B) t²
C) t³
D) t⁴
32. If a force of 50 N is applied to an object moving at a constant velocity of 10 m/s in the same direction, what is the power developed?
A) 5 W
B) 500 W
C) 5000 W
D) 50 W
33. Which of the following is NOT a non-conservative force?
A) Viscous force
B) Frictional force
C) Gravitational force
D) Air resistance
34. In the absence of non-conservative forces, the sum of kinetic and potential energy of a particle moving under a central force is:
A) Always increasing
B) Always decreasing
C) Constant
D) Zero
35. A person climbs a hill of height 100 m. If the person's mass is 60 kg, what is the work done against gravity? (g = 10 m/s²)
A) 600 J
B) 6000 J
C) 60000 J
D) 600000 J
36. When a conservative force does positive work on a system, the potential energy of the system:
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero
37. A block of mass 2 kg is moving with a velocity of 5 m/s. What is its kinetic energy?
A) 10 J
B) 25 J
C) 50 J
D) 12.5 J
38. Consider a pendulum swinging. At the extreme positions, the velocity is zero. What is the nature of mechanical energy at these points?
A) Maximum kinetic energy, minimum potential energy
B) Minimum kinetic energy, maximum potential energy
C) Zero kinetic energy, maximum potential energy
D) Maximum kinetic energy, zero potential energy
39. If a system is subjected to only conservative forces, then the work done by these forces is equal to the change in:
A) Kinetic energy
B) Potential energy
C) Total mechanical energy
D) Angular momentum
40. A spring is stretched by 2 cm. If the spring constant is 100 N/m, calculate the potential energy stored in the spring.
A) 0.02 J
B) 0.04 J
C) 0.01 J
D) 0.005 J
41. When a body falls freely under gravity from a certain height, its mechanical energy:
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero
42. Which of the following is a conservative force?
A) Friction
B) Air resistance
C) Gravitational force
D) Tension in a spring
43. Total mechanical energy (E) of a system is the sum of:
A) Kinetic energy and potential energy
B) Work done and energy
C) Force and displacement
D) Momentum and velocity
44. Conservation of mechanical energy states that in the absence of non-conservative forces, the total mechanical energy of a system remains:
A) Increases
B) Decreases
C) Constant
D) Varies with time
45. A machine does 1200 Joules of work in 10 seconds. What is its average power?
A) 120 J/s
B) 12000 W
C) 120 W
D) 0.0083 W
46. If a force F acts on an object moving with velocity v, the instantaneous power developed by the force is given by:
A) P = F + v
B) P = F - v
C) P = F * v
D) P = F / v
47. 1 horsepower (hp) is approximately equal to:
A) 746 Watts
B) 1000 Watts
C) 550 Watts
D) 100 Watts
48. Which of the following statements about power is correct?
A) Power is a scalar quantity.
B) Power is a vector quantity.
C) Power depends on the direction of force.
D) Power is the total work done.
49. An electric motor lifts a load of 10 kg by a height of 5 meters in 2 seconds. If g = 10 m/s², calculate the power developed by the motor.
A) 250 W
B) 500 W
C) 100 W
D) 50 W
50. Power is defined as the rate of doing work. If work (W) is done in time (t), what is the formula for average power?
A) P = W * t
B) P = W / t
C) P = t / W
D) P = W + t
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