A particle of mass m is attached to a light string of length I, the other end of which is fixed. Initially, the string is kept horizontal and the particle is given an upward velocity v. The particle is just able to complete a circle.

(a) The string becomes slack when the particle reaches its highest point.

(b) The velocity of the particle becomes zero at the highest point.

(c) The kinetic energy of the ball in its initial position was \(\frac{1}{2}mv^2 = mgl.\)

(d) The particle again passes through the initial position.

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. (a) and (d)

Subtopic:  Work Energy Theorem |
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The kinetic energy of a particle continuously increases with time. Then we can conclude that:

(a) The resultant force on the particle must be parallel to the velocity at all instants.
(b) The resultant force on the particle must be at an angle less than \(90^{\circ}\) all the time.
(c) Its height above the ground level must continuously decrease.
(d) The magnitude of its linear momentum is increasing continuously.

Choose the correct option:
1. (a) and (b)
2. (b) and (c)
3. (b) and (d)
4. (c) and (d)

Subtopic:  Work Energy Theorem |
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One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is \(\frac{1}{2}\)kx2. The possible causes are

(a) the spring was initially compressed by a distance and was finally in its natural length

(b) it was initially stretched by a distance of x and was in its natural length

(b) it was initially in its natural length and finally in the compressed position

(d) it was initially in its natural length and finally in a stretched position

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

Subtopic:  Elastic Potential Energy |
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A block of mass M is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F. The kinetic energy of the block increases by 20 J in 1 s.

1. The tension in the string is Mg

2. The tension in the string is F

3. The work done by the tension on the block is 20 J in the above 1 s

4. The work done by the force of gravity is –20 J in tie above 1 s

Subtopic:  Work Energy Theorem |
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A bullet hits a block kept at rest on a smooth horizontal surface and gets embedded into it. Which of the following does not change?

1. linear momentum of the block
2. kinetic energy of the block
3. gravitational potential energy of the block
4. temperature of the block
Subtopic:  Collisions |
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A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass:

1. of the box remains constant.
2. of the box plus the ball system remains constant.
3. of the ball remains constant.
4. of the ball relative to the box remains constant.

Subtopic:  Collisions |
 70%
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A body at rest breaks into two pieces of equal masses. The parts will move:

1. in the same direction.
2. along different lines.
3. in opposite directions with equal speeds.
4. in opposite directions with unequal speeds.

Subtopic:  Collisions |
 83%
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The quantities remaining constant in a collision are:

1. momentum, kinetic energy and temperature
2. momentum and kinetic energy but not temperature
3. momentum and temperature but not kinetic energy
4. momentum, but neither kinetic energy nor temperature

Subtopic:  Collisions |
 67%
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In an elastic collision:

1. the initial kinetic energy is equal to the final kinetic energy.
2. the final kinetic energy is less than the initial kinetic energy.
3. the kinetic energy remains constant.
4. the kinetic energy first increases then decreases.

Subtopic:  Collisions |
 72%
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In an inelastic collision:

1. The initial kinetic energy is equal to the final kinetic energy.
2. The final kinetic energy is less than the initial kinetic energy.
3. The kinetic energy remains constant.
4. The kinetic energy first increases and then decreases.

Subtopic:  Collisions |
 79%
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