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.

Subtopic:  Center of Mass |
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Consider the following two statements:

(A) Linear momentum of the system remains constant.
(B) Centre of mass of the system remains at rest.

1. A implies B and B implies A

2. A does not imply B and B does not imply A

3. A implies B but B does not imply A

4. B implies A but A does not imply B

Subtopic:  Center of Mass |
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Consider the following two statements :

(A) Linear momentum of a system of particles is zero.
(B) Kinetic energy of a system of particles is zero.

1. A implies B and B implies A

2. A does not imply B and B does not imply A

3. A implies B but B does not imply A

4. B implies A but A does not imply B

Subtopic:  Center of Mass |
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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. ≤ R

3. > R

4. ≥ R

Subtopic:  Center of Mass |
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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:

1.  inside the circular plate

2. inside the square plate

3. at the point of contact

4. outside the system

Subtopic:  Center of Mass |
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Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration $$\overrightarrow a$$. The centre of mass has an acceleration:

1. zero

2. $$\frac{1}{2}\overrightarrow a$$

3. $$\overrightarrow a$$

4. $$2\overrightarrow a$$

Subtopic:  Center of Mass |
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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

Subtopic:  Center of Mass |
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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:

1. heavier piece

2. lighter piece

3. does not shift horizontally

4. depends on the vertical velocity at the time of breaking

Subtopic:  Center of Mass |
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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

Subtopic:  Center of Mass |
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The centre of mass of a system of particles is at the origin. It follows that

(a) the number of particles to the right of the origin is equal to the number of particles to the left

(b) the total mass of the particles to the right of the origin is same as the total mass to the left of the origin

(c) the number of particles on X-axis should be equal to the number of particles on Y-axis

(d) if there is a particle on the positive X-axis, there must be at least one particle on the negative X-axis

Choose the correct option:

1. (a), (b) and (c)

2. (a), (b) and (d)

3. All of these

4. None of these

Subtopic:  Center of Mass |