A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
1. | \(60^{\circ}\) from vertical. | inclined at an angle of
2. | the mass is at the highest point. |
3. | the wire is horizontal. |
4. | the mass is at the lowest point. |
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. \(\frac{5}{9}\)
2. \(\frac{1}{9}\)
3. \(\frac{8}{9}\)
4. \(\frac{4}{9}\)
An object of mass \(500\) 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 \(x=8\) m and \(x=12\) m would have the respective values of nearly:
1. | \(18\) m/s and \(22.4\) m/s | 2. | \(23\) m/s and \(22.4\) m/s |
3. | \(23\) m/s and \(20.6\) m/s | 4. | \(18\) m/s and \(20.6\) m/s |
Water falls from a height of 60m at the rate of 15kg/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/)
1. 8.1 kW 2. 10.2 kW
3. 12.3 kW 4. 7.0 kW
1. | \(23500\) | 2. | \(23000\) |
3. | \(20000\) | 4. | \(34500\) |
A particle of mass \(4M\) kg at rest splits into two particles of mass \(M\) and \(3M.\) The ratio of the kinetic energies of mass \(M\) and \(3M\) would be:
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. | \(\frac12u\sqrt{\frac{k}{m}}\) |