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 \(20.6~\text {m/s}\) |
| 1. | \(10~\text{J}\) | 2. | \(16~\text J\) |
| 3. | \(4~\text J\) | 4. | \(6~\text J\) |
| 1. | \(30\) cm | 2. | \(27\) cm |
| 3. | \(24\) cm | 4. | \(28\) cm |
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. | \((\text{i})~-10~\text{J};\) \((\text{ii})~-8.75~\text{J}\) |
| 1. | \(7.5~\text m\) | 2. | \(10~\text m\) |
| 3. | \(2.5~\text m\) | 4. | \(5~\text m\) |
| 1. | \(W_1=W_2=W_3\) | 2. | \(W_1>W_2>W_3\) |
| 3. | \(W_1>W_3>W_2\) | 4. | \(W_1<W_2<W_3\) |
A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
| 1. | inclined at an angle of \(60^{\circ}\) from vertical. |
| 2. | the mass is at the highest point. |
| 3. | the wire is horizontal. |
| 4. | the mass is at the lowest point. |