Q. No.A body of mass (\(4m\)) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (\(m\)) move perpendicular to each other with equal speeds (\(u\)). The total kinetic energy generated due to explosion is:
| 1. | \(mu^2\) | 2. | \(1.5~mu^2\) |
| 3. | \(2~mu^2\) | 4. | \(3~mu^2\) |
A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2~\text{kg}.\) Hence the particle is displaced from the position \((2 \hat{i} + \hat{k})\) metre to the position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) metre. The work done by the force on the particle is:
1. \(6~\text{J}\)
2. \(13~\text{J}\)
3. \(15~\text{J}\)
4. \(9~\text{J}\)
1. \(14~\text{J}\)
2. \(8~\text{J}\)
3. \(6~\text{J}\)
4. \(10~\text{J}\)
1. \(20~\text{J}\)
2. \(30~\text{J}\)
3. \(5~\text{J}\)
4. \(25~\text{J}\)
| 1. | \(10~\text{J}\) | 2. | \(16~\text J\) |
| 3. | \(4~\text J\) | 4. | \(6~\text J\) |
(Take \(\sqrt2\cong1.4\))
| 1. | \(0.5~\text{ms}^{-1}\) | 2. | \(1~\text{ms}^{-1}\) |
| 3. | \(2.5~\text{ms}^{-1}\) | 4. | \(4.8~\text{ms}^{-1}\) |
| 1. | \(30\) cm | 2. | \(27\) cm |
| 3. | \(24\) cm | 4. | \(28\) cm |
An object of mass \(500~\text g\) initially at rest is acted upon by a variable force whose \(x\)-component varies with \(x\) in the manner shown. The velocities of the object at the points \(x=8~\text m\) and \(x=12~\text m\) would have the respective values of nearly:
| 1. | \(18~\text {m/s}\) and \(22.4~\text {m/s}\) | 2. | \(23~\text {m/s}\) and \(22.4~\text {m/s}\) |
| 3. | \(23~\text {m/s}\) and \(20.6~\text {m/s}\) | 4. | \(18~\text {m/s}\) and \(20.6~\text {m/s}\) |
A body initially at rest and sliding along a frictionless track from a height \(h\) (as shown in the figure) just completes a vertical circle of diameter \(\mathrm{AB}= D.\) The height \({h}\) is equal to:
| 1. | \({3\over2}D\) | 2. | \(D\) |
| 3. | \({7\over4}D\) | 4. | \({5\over4}D\) |
Consider a drop of rainwater having a mass of \(1~\text{gm}\) falling from a height of \(1~\text{km}.\) It hits the ground with a speed of \(50~\text{m/s}.\) Take \(g\) as constant with a value \(10~\text{m/s}^2.\) The work done by the
(i) gravitational force and the (ii) resistive force of air is:
| 1. | \((\text{i})~1.25~\text{J};\) \((\text{ii})~-8.25~\text{J}\) |
| 2. | \((\text{i})~100~\text{J};\) \((\text{ii})~8.75~\text{J}\) |
| 3. | \((\text{i})~10~\text{J};\) \((\text{ii})~-8.75~\text{J}\) |
| 4. | \((\text{i})~-10~\text{J};\) \((\text{ii})~-8.75~\text{J}\) |
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