Q. No.Position of centre of mass of a triangular lamina as shown in the figure is:
2. at the point \(G\).
3. at the point \(L\).
4. can't be determined.
From a disc of radius \(R,\) a disc of radius \(\frac{R}{2}\) is taken out as shown in the figure. The position of the centre of mass of the remaining disc is on:
1. \({OA}\)
2. \({OB}\)
3. \({OC}\)
4. \({OD}\)
Two bodies of mass \(1\) kg and \(3\) kg have position vectors \(\hat{i}+2\hat{j}+\hat{k}\) and \(-3\hat{i}-2\hat{j}+\hat{k}\) respectively. The centre of mass of this system has a position vector:
1. \(-2\hat{i}+2\hat{k}\)
2. \(-2\hat{i}-\hat{j}+\hat{k}\)
3. \(2\hat{i}-\hat{j}-2\hat{k}\)
4. \(-\hat{i}+\hat{j}+\hat{k}\)
Three particles of masses \(100~\text{g}\), \(150~\text{g}\), and \(200~\text{g}\) respectively are placed at the vertices of an equilateral triangle of a side \(0.5~\text{m}\) long. What is the position of the centre of mass of three particles?
| 1. | \(\left(\dfrac{5}{18} , \dfrac{1}{3 \sqrt{3}}\right) \) | 2. | \(\left(\dfrac{1}{4} , 0\right) \) |
| 3. | \(\left(0 , \dfrac{1}{4}\right) \) | 4. | \(\left(\dfrac{1}{3 \sqrt{3}} , \dfrac{5}{18}\right) \) |
| Assertion (A): | The centre-of-mass of a proton and an electron, released from their respective positions remains at rest. |
| Reason (R): | The centre-of-mass remains at rest if no external force is applied. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
For which of the following does the centre of mass lie outside the body?
1. A pencil
2. A shotput
3. A dice
4. A bangle
The centre-of-mass of a thin, uniform triangular lamina lies at its:
1. orthocenter
2. circumcenter
3. centroid
4. incenter
| 1. | \(40~\text{cm}\) from the \(2~\text{kg}\) particle |
| 2. | \(60~\text{cm}\) from the \(3~\text{kg}\) particle |
| 3. | \(60~\text{cm}\) from the \(2~\text{kg}\) particle |
| 4. | \(20~\text{cm}\) from the \(3~\text{kg}\) particle |
Three masses are placed on the \(x\)-axis: \(300~\text{g}\) at origin, \(500~\text{g}\) at \(x= 40~\text{cm}\) and \(400~\text{g}\) at \(x= 70~\text{cm}.\) The distance of the centre of mass from the origin is:
1. \(45~\text{cm}\)
2. \(50~\text{cm}\)
3. \(30~\text{cm}\)
4. \(40~\text{cm}\)
| Assertion (A): | The acceleration of the centre-of-mass of a system of particles does not depend on the internal forces between the particles. |
| Reason (R): | The net force acting on the system does not get any contribution from internal forces as the latter cancel in pairs, due to Newton's third law. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
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