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.
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From a disc of radius \(R,\) a disc of radius \(\dfrac{R}{2}\) 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. \(-\hat{i}+\hat{j}+\hat{k}\)
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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. | \(\left(\dfrac{1}{3 \sqrt{3}} , \dfrac{5}{18}\right) \) |
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
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| 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 |
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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. \(40~\text{cm}\)
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| 1. | \(OW\) | 2. | \(OX\) |
| 3. | \(OY\) | 4. | \(OZ\) |
A child sits stationary at one end of a long trolley moving uniformly with a speed \(v\) on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, then the speed of the centre of mass of the (trolley + child) system:
1. decreases
2. increases
3. remains unchanged
4. none of these
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1. \(0.4\) m from \(m_{A}\)
2. \(0.6\) m from \(m_{A}\)
3. \(0.5\) m from \(m_{A}\)
4. \(0.7\) m from \(m_{A}\)
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