Q. No.1. \(2v\)
2. zero
3. \(v\)
4. \(4v\)
| 1. | \(5~ \text m\) | 2. | \(\dfrac{10}{3} \mathrm{~m}\) |
| 3. | \(\dfrac{20}{3} \mathrm{~m}\) | 4. | \(10~ \text m\) |
| 1. | \(2(\hat{i}+\hat{j})\) | 2. | \(\hat{i}+\hat{j}\) |
| 3. | \(\frac{2}{3}(\hat{i}+\hat{j})\) | 4. | \(\frac{4}{3}(\hat{i}+\hat{j})\) |
Two particles of mass \(5~\text{kg}\) and \(10~\text{kg}\) respectively are attached to the two ends of a rigid rod of length \(1~\text{m}\) with negligible mass. The centre of mass of the system from the \(5~\text{kg}\) particle is nearly at a distance of:
1. \(50~\text{cm}\)
2. \(67~\text{cm}\)
3. \(80~\text{cm}\)
4. \(33~\text{cm}\)
Which of the following statements are correct?
| (a) | centre of mass of a body always coincides with the centre of gravity of the body . |
| (b) | centre of gravity of a body is the point about which the total gravitational torque on the body is zero. |
| (c) | a couple on a body produce both translational and rotation motion in a body. |
| (d) | mechanical advantage greater than one means that small effort can be used to lift a large load. |
| 1. | (a) and (b) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (b) and (d) |
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. \(40~\text{cm}\)
Two persons of masses \(55~\text{kg}\) and \(65~\text{kg}\) respectively, are at the opposite ends of a boat. The length of the boat is \(3.0~\text{m}\) and weighs \(100~\text{kg}.\) The \(55~\text{kg}\) man walks up to the \(65~\text{kg}\) man and sits with him. If the boat is in still water, the centre of mass of the system shifts by:
1. \(3.0~\text{m}\)
2. \(2.3~\text{m}\)
3. zero
4. \(0.75~\text{m}\)
| 1. | \(\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}={k}\) |
| 2. | \(\omega_{1}x_{1}=\omega_{2}x_{2}=\omega_{3}x_{3}={k}\) |
| 3. | \(\omega_{1}x_{1}^{2}=\omega_{2}x_{2}^{2}=\omega_{3}x_{3}^{2}={k}\) |
| 4. | \(\omega_{1}^{2}x_{1}=\omega_{2}^{2}x_{2}=\omega_{3}^{2}x_{3}={k}\) |
1. \(1~\text{rad/s}\)
2. \(5~\text{rad/s}\)
3. \(10~\text{rad/s}\)
4. \(15~\text{rad/s}\)
| 1. | along the axis of rotation |
| 2. | along the radius, away from the centre |
| 3. | along the radius towards the centre |
| 4. | along the tangent to its position |
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