Q. No.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.
1. \(20~\text{J}\)
2. \(30~\text{J}\)
3. \(5~\text{J}\)
4. \(25~\text{J}\)
When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:
1. \(1:2\sqrt{3}\)
2. \(1:\sqrt{2}\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{3}\)
Body \(\mathrm{A}\) of mass \(4m\) moving with speed \(u\) collides with another body \(\mathrm{B}\) of mass \(2m\) at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body \(\mathrm{A}\) is:
| 1. | \(\dfrac{5}{9}\) | 2. | \(\dfrac{1}{9}\) |
| 3. | \(\dfrac{8}{9}\) | 4. | \(\dfrac{4}{9}\) |
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 \(20.6~\text {m/s}\) |
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine?
(g = 10 m/s2)
1. 8.1 kW
2. 10.2 kW
3. 12.3 kW
4. 7.0 kW
| 1. | \(1\times 10^{5}~\text J\) | 2. | \(36\times 10^{7}~\text J\) |
| 3. | \(36\times 10^{4}~\text J\) | 4. | \(36\times 10^{5}~\text J\) |
(Take \(g=10\) ms–2)
1. \(23500\)
2. \(23000\)
3. \(20000\)
4. \(34500\)
1. \(3:1\)
2. \(1:4\)
3. \(1:1\)
4. \(1:3\)
A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
| 1. | \(u\sqrt{\frac{m}{k}}\) | 2. | \(4u\sqrt{\frac{m}{k}}\) |
| 3. | \(2u\sqrt{\frac{m}{k}}\) | 4. | \(\dfrac12u\sqrt{\frac{k}{m}}\) |
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