Q. No.Consider the following two statements:
A:
The linear momentum of a system of particles is zero.
B:
The 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.
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:
| 1. | inside the circular plate |
| 2. | inside the square plate |
| 3. | at the point of contact |
| 4. | outside the system |
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:
| 1. | heavier piece |
| 2. | lighter piece |
| 3. | does not shift horizontally |
| 4. | depends on the vertical velocity at the time of breaking |
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
| (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
A body has its center of mass at the origin. The \(x\text-\)coordinates of the particles:
| (a) | maybe all positive |
| (b) | maybe all negative |
| (c) | maybe all non-negative |
| (d) | maybe positive for some cases and negative in other cases |
Choose the correct option from the given ones:
| 1. | (a) and (b) only |
| 2. | (b) and (c) only |
| 3. | (c) and (d) only |
| 4. | All of these |
In which of the following cases the centre of mass of a rod is certainly not at its centre?
| a. | the density continuously increases from left to right. |
| b. | the density continuously decreases from left to right. |
| c. | the density decreases from left to right upto the centre and then increases. |
| d. | the density increases from left to right upto the centre and then decreases. |
Choose the correct options:
| 1. | (a) and (b) |
| 2. | (a), (b) and (c) |
| 3. | all of these |
| 4. | none of these |
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