A particle is rotated in a vertical circle by connecting it to a string of length I and keeping the other end of the string fixed. The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is

1. \(\sqrt{\mathrm{g} l}\)

2. \(\sqrt{2 \mathrm{~g} l}\)

3. \(\sqrt{3 \mathrm{~g} l}\)

4. \(\sqrt{5 \mathrm{~g} l}\)

A heavy stone is thrown from a cliff of height \(h\) in a given direction. The speed with which it hits the ground:

Choose the correct option:

The total work done on a particle is equal to the change in its kinetic energy:

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that
a. its velocity is constant
b. its acceleration is constant
c. its kinetic energy is constant
d. it moves in a circular path
Choose the correct option:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. All of these

Consider two observers moving with respect to each other at a speed v along a straight line. They observe a block of mass m moving a distance I on a rough surface. The following quantities will be same as observed by the two observers

1. kinetic energy of the block at time t

2. work done by friction

3. total work done on the block

4. acceleration of the block

You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase does not depend on:

Choose the correct option:

No work is done by a force on an object if:

Choose the correct option:

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)

The kinetic energy of a particle continuously increases with time. Then we can conclude that:

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

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