Consider the following two equations:

(A) \(\vec{R}=\frac{1}{M} \sum_{i} m_{i} \overrightarrow{r_{i}}\)     and  (B) \(\vec{a}_{C M}=\frac{\vec{F}}{M}\)

In a non-inertial frame:

1. both are correct.

2. both are wrong.

3. A is correct but B is wrong.

4. B is correct but A is wrong.

Consider the following two statements:

Consider the following two statements:

All the particles of a body are situated at a distance \(R\) from the origin. The distance of the centre of mass of the body from the origin is:
1. \(=R\)
2. \(\leq R\)
3. \(>R\)
4. \(\geq R \)

A circular plate of diameter \(d\) is kept in contact with a square plate of edge \(d\) as shown in the figure. The density of the material and the thickness are the same everywhere. The centre of mass of the composite system will be:

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:

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