A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its center of gravity is 1.05 m behind the front axle. The force exerted by the level ground on each front wheel and each back wheel is respectively:
1. 2680 N, 5145 N
2. 5145 N, 3675 N
3. 5145 N, 5145 N
4. 3675 N, 5145 N

Given the moment of inertia of a disc of mass \(M\) and radius \(R\) about any of its diameters to be \(\frac{MR^{2}}{4},\) then the moment of inertia about an axis normal to the disc passing through a point on its edge is:
1. \(\frac{3}{2}MR^{2}\)
2. \(\frac{1}{4}MR^{2}\)
3. \(\frac{2}{5}MR^{2}\)
4. \(\frac{7}{5}MR^{2}\)

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. The angular velocity of the solid sphere is:

A child stands at the centre of a turntable with his arms outstretched. The turntable is set to rotate with an angular speed of \(40\) rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to \(2\over 5\) times the initial value?
1. \(160\) rev/min
2. \(150\) rev/min
3. \(100\) rev/min
4. \(120\) rev/min

A rope of negligible mass is wound around a hollow cylinder of mass \(3\) kg and radius \(40\) cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of \(30\) N?
(Assume that there is no slipping.)
1. \(21\) rad/s²
2. \(24\) rad/s²
3. \(20\) rad/s²
4. \(25\) rad/s²

To maintain a rotor at a uniform angular speed of \(200\) rad s^-1, an engine needs to transmit a torque of \(180\) N-m. What is the power required by the engine?
1. \(33\) kW
2. \(36\) kW
3. \(28\) kW
4. \(76\) kW

A meter stick is balanced on a knife edge at its center. When two coins, each of the mass \(5\) gm are put one on top of the other at the \(12.0\) cm mark, the stick is found to be balanced at \(45.0\) cm. What is the mass of the meter stick?
1. \(66\) g
2. \(56\) g
3. \(76\) g
4. \(79\) g

The oxygen molecule has a mass of 5.30 x 10^-26 kg and a moment of inertia of 1.94 x 10^-46 kg m² about an axis through its center perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

1. $5.7\times {10}^{11} rad s^{-1}$

2. $5.7\times {10}^{12} rad s^{-1}$

3. $6.7\times {10}^{11} rad s^{-1}$

4.$6.7\times {10}^{12} rad s^{-1}$ 

A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90 cm to 20 cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m². What is his new angular speed?

1. 60 rev/min
2. 57.0 rev/min
3. 58.8 rev/min
4. 60.1 rev/min

A bullet of mass \(10\) g and speed \(500\) m/s is fired into a door and gets embedded exactly at the center of the door. The door is \(1.0\) m wide and weighs \(12\) kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it is:
1. \(0.122\) rad/s
2. \(0.625\) rad/s
3. \(0.231\) rad/s
4. \(0.191\) rad/s