Conservation of mechanical energy, conservative and non conservative forces, motion in a vertical circle - Question Bank

1. When a body moves in a vertical circle, the work done by tension in the string is:
A) Always positive
B) Always negative
C) Always zero
D) Can be positive or negative
2. In vertical circular motion, at the lowest point, the tension T and the gravitational force mg provide the centripetal force. The equation is:
A) T - mg = mv^2/L
B) T + mg = mv^2/L
C) mg - T = mv^2/L
D) T = mv^2/L
3. Which of the following is a consequence of the law of conservation of mechanical energy?
A) Total energy of the system always increases.
B) Kinetic energy is always converted to potential energy.
C) The sum of kinetic and potential energy remains constant.
D) Non-conservative forces do no work.
4. If a particle moves in a vertical circle, the component of gravitational force along the instantaneous velocity is:
A) Always zero
B) Non-zero and does work
C) Zero only at the top and bottom
D) Zero only at the horizontal points
5. The work done by gravity in moving an object from height h1 to h2 is:
A) mg(h1 - h2)
B) mg(h2 - h1)
C) mgh1
D) mgh2
6. In vertical circular motion, the speed at the highest point is v_top. What is the speed at the lowest point if the radius is L?
A) v_lowest = sqrt(v_top^2 + 2gL)
B) v_lowest = sqrt(v_top^2 + gL)
C) v_lowest = sqrt(v_top^2 + 4gL)
D) v_lowest = v_top
7. If the work done by a force is path-dependent, the force is:
A) Conservative
B) Non-conservative
C) Central force
D) Electrostatic force
8. For a particle to complete a vertical circle, the minimum speed required at the highest point is:
A) sqrt(gL)
B) sqrt(2gL)
C) sqrt(3gL)
D) sqrt(5gL)
9. What is the potential energy of a particle at height 'h' above the ground?
A) 1/2 mgh
B) mgh
C) mgh^2
D) mgh/2
10. Which of the following is NOT a conservative force?
A) Gravitational force
B) Spring force
C) Magnetic force
D) Frictional force
11. If a string breaks at the lowest point of a vertical circle, the object will move:
A) Vertically upwards
B) In a straight line tangentially
C) In a parabolic path
D) In a spiral path
12. The conservation of mechanical energy holds true when:
A) Only non-conservative forces are present.
B) Non-conservative forces do zero net work.
C) The system is not isolated.
D) The velocity is constant.
13. When a spring is compressed or stretched, the work done is stored as:
A) Kinetic energy
B) Gravitational potential energy
C) Elastic potential energy
D) Thermal energy
14. A particle is moving in a vertical circle. At the highest point, the net force is:
A) Towards the center
B) Away from the center
C) Tangential
D) Zero
15. Which type of force is always associated with a change in potential energy?
A) Non-conservative force
B) Conservative force
C) Frictional force
D) Air resistance
16. In vertical circular motion, if the velocity at the highest point is sqrt(gL), what is the tension at the lowest point?
A) 3mg
B) 4mg
C) 5mg
D) 6mg
17. If the net force acting on an object is conservative, then:
A) Mechanical energy is not conserved.
B) Mechanical energy is conserved.
C) Potential energy increases.
D) Kinetic energy decreases.
18. A block is pushed across a rough floor. The work done by friction is converted into:
A) Potential energy
B) Kinetic energy
C) Heat and sound energy
D) Stored elastic energy
19. The work done by a non-conservative force on a system is equal to the change in:
A) Potential energy
B) Kinetic energy
C) Mechanical energy
D) Total energy
20. What is the condition for an object to just complete a vertical circle when tied to a string of length L?
A) Velocity at the top >= sqrt(gL)
B) Velocity at the top <= sqrt(gL)
C) Velocity at the top = 0
D) Velocity at the top >= sqrt(2gL)
21. A child swings on a swing. Assuming no air resistance, the mechanical energy of the child is:
A) Increased
B) Decreased
C) Conserved
D) Converted to heat
22. Which of the following is a potential energy function associated with a conservative force?
A) F = -kx
B) F = -mu N
C) F = bv
D) F = mr omega^2
23. In motion in a vertical circle, what is the speed at the lowest point if the speed at the highest point is v_top and the radius is L?
A) v_lowest = sqrt(v_top^2 + 4gL)
B) v_lowest = sqrt(v_top^2 + 2gL)
C) v_lowest = sqrt(v_top^2 + gL)
D) v_lowest = sqrt(v_top^2)
24. If a particle moves from point A to point B and the work done by the net force is zero, then the change in kinetic energy is:
A) Positive
B) Negative
C) Zero
D) Cannot be determined
25. Which force is responsible for maintaining circular motion, but does no work if the motion is perfectly circular?
A) Frictional force
B) Centripetal force
C) Tension force
D) Gravitational force
26. The law of conservation of mechanical energy is a special case of the law of conservation of:
A) Momentum
B) Charge
C) Mass
D) Total energy
27. When a block slides down a rough inclined plane, the work done by gravity is converted into:
A) Kinetic energy only
B) Potential energy only
C) Heat and kinetic energy
D) Heat and potential energy
28. Which of the following is a condition for completing a vertical circle with a string?
A) Speed at the top must be greater than sqrt(gL)
B) Speed at the top must be equal to sqrt(gL)
C) Speed at the top must be less than sqrt(gL)
D) Speed at the top must be zero
29. What is the work done by the gravitational force when an object moves from a height h1 to h2?
A) mg(h2 - h1)
B) mg(h1 - h2)
C) mgh1
D) mgh2
30. If a conservative force does positive work, the potential energy of the system:
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero
31. In motion in a vertical circle, at which point is the tension in the string the maximum?
A) Highest point
B) Lowest point
C) Midpoint (horizontal level)
D) Point at 45 degrees from the bottom
32. Consider a ball rolling down a frictionless inclined plane. Its mechanical energy is:
A) Increased
B) Decreased
C) Conserved
D) Converted to heat
33. The work done by friction on a moving object is always:
A) Positive
B) Negative
C) Zero
D) Can be positive or negative
34. Which of the following is a unit of energy?
A) Newton
B) Joule
C) Watt
D) Pascal
35. If the work done by a force is independent of the path, the force is:
A) Non-conservative
B) Conservative
C) Frictional
D) Viscous
36. What is the nature of the force exerted by an ideal spring?
A) Non-conservative
B) Conservative
C) Always dissipative
D) Dependent on velocity
37. A stone is tied to a string and whirled in a vertical circle. If the speed at the top is just sufficient to complete the circle, the tension in the string at the top is:
A) mg
B) 2mg
C) Zero
D) 3mg
38. For a particle undergoing motion in a vertical circle, the tension in the string at the highest point is minimum. What is the condition if the particle is just completing the circle?
A) Tension is zero
B) Tension is equal to centripetal force
C) Tension is equal to mg
D) Tension is equal to 2mg
39. When an object is thrown vertically upwards, which force is non-conservative and opposes its motion?
A) Gravitational force
B) Air resistance
C) Centripetal force
D) Normal force
40. Which of the following represents the change in kinetic energy of a particle when it moves from point A to point B under the influence of a conservative force F?
A) Delta KE = - Delta PE
B) Delta KE = Delta PE
C) Delta KE = - W_non-conservative
D) Delta KE = W_non-conservative
41. If a body is moving in a vertical circle with radius 'r', and the string breaks at the highest point, in what direction will the body move?
A) Vertically downwards
B) Horizontally
C) Tangentially
D) In a parabolic path
42. In the context of motion in a vertical circle, what is the condition at the lowest point if the object is just able to complete the circle?
A) Tension = 6mg
B) Tension = 5mg
C) Tension = 4mg
D) Tension = 3mg
43. What is the minimum speed a body must have at the highest point of a vertical circle to complete the circle without the string becoming slack?
A) sqrt(gL)
B) sqrt(2gL)
C) sqrt(3gL)
D) sqrt(5gL)
44. Consider a block sliding down a rough inclined plane. Which force is non-conservative in this scenario?
A) Gravitational force
B) Normal force
C) Frictional force
D) Component of gravity parallel to the plane
45. When a non-conservative force does work on a system, what happens to the total mechanical energy?
A) It remains constant.
B) It increases.
C) It decreases.
D) It can increase or decrease depending on the force.
46. Which of the following is an example of a non-conservative force?
A) Spring force
B) Electric force
C) Viscous drag
D) Centripetal force
47. If a system is isolated and only conservative forces are acting, what happens to its total mechanical energy?
A) It increases.
B) It decreases.
C) It remains constant.
D) It fluctuates randomly.
48. Which of the following is a characteristic of a conservative force?
A) The work done by the force depends on the path taken.
B) The work done by the force in a round trip is always zero.
C) Energy is lost due to the force.
D) The force is always proportional to velocity.
49. Identify a force that is generally considered conservative.
A) Friction
B) Air resistance
C) Gravitational force
D) Tension in a string
50. Which of the following conditions must be met for the law of conservation of mechanical energy to be applicable?
A) Only conservative forces do work.
B) Only non-conservative forces do work.
C) Both conservative and non-conservative forces do work.
D) No forces do work.
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