Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration \(\vec{a}\). The centre of mass has an acceleration:
1. zero
2. \(\vec{a}/2\)
3. \(\vec{a}\)
4. \(2\vec{a}\)

A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface. The acceleration of the centre

1. is maximum when h = 0

2. is maximum when h = R

3. is maximum when h = 2R

4. is independent of h

A body falling vertically downwards under gravity breaks into two parts of unequal masses. The centre of mass of the two parts taken together shifts horizontally towards:

A heavy ring of mass m is clamped on the periphery of a light circular disc. A small particle having equal mass is clamped at the centre of the disc. The system is rotated in such a way that the centre moves in a circle of radius r with a uniform speed v. We conclude that an external force

1. \(\frac{mv^2}{r}\) must be acting on the central particle

2. \(\frac{2mv^2}{r}\) must be acting on the central particle

3. \(\frac{2mv^2}{r}\) must be acting on the system

4. \(\frac{2mv^2}{r}\) must be acting on the ring

Choose the correct option:
1. (a), (b) and (c)
2. (a), (b) and (d)
3. All of these
4. none of these

A body has its centre of mass at the origin. The x–coordinates of the particles:

(a) may be all positive

(b) may be all negative

(c) may be all non-negative

(d) may be positive for some case and negative in other cases

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

In which of the following cases the centre of mass of a rod is certainly not at its centre?
 

Choose the correct options:

If the external forces acting on a system have zero resultant, the centre of mass:

(a) must not move

(b) must not accelerate

(c) may move

(d) may accelerate

Choose the correct options:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

A nonzero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be \(v_0\) and \(a_0\) at an instant \(t.\) It is possible that:
(a) \(v_0=0,\) \(a_0=0\)
(b) \(v_0=0,\) \(a_0 \neq0\)
(c) \(v_0 \neq0,\) \(a_0=0\)
(d) \(v_0 \neq0,\) \(a_0 \neq0\)
Choose the correct options:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (b) and (d)

Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls while in the air: