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1.

Two particles of mass \(5~\text{kg}\) and \(10~\text{kg}\) respectively are attached to the two ends of a rigid rod of length \(1~\text{m}\) with negligible mass. The centre of mass of the system from the \(5~\text{kg}\) particle is nearly at a distance of:
1. \(50~\text{cm}\)
2. \(67~\text{cm}\)
3. \(80~\text{cm}\)
4. \(33~\text{cm}\)

2.

A wheel has an angular acceleration of \(3.0~\text{rad/s}^2\) and an initial angular speed of \(2.00~\text{rad/s}.\) In a time of \(2~\text s,\) it has rotated through an angle (in radians) of:
1. \(6\)
2. \(10\)
3. \(12\)
4. \(4\)

3.

Five particles of mass \(2\) kg each are attached to the circumference of a circular disc of a radius of \(0.1\) m and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane will be:
1. \(1\) kg-m²
2. \(0.1\) kg-m²
3. \(2\) kg-m²
4. \(0.2\) kg-m²

4.

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

5.

A solid sphere of mass \(M\) and the radius \(R\) is in pure rolling with angular speed \(\omega\) on a horizontal plane as shown in the figure. The magnitude of the angular momentum of the sphere about the origin \(O\) is:
                 
1. \(\frac{7}{5} M R^{2} \omega\)
2. \(\frac{3}{2} M R^{2} \omega\)
3. \(\frac{1}{2} M R^{2} \omega\)
4. \(\frac{2}{3} M R^{2} \omega\)$$

6.

A wheel is rotating about an axis through its centre at \(720~\text{rpm}.\) It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally. The value of torque in \((\text{N-m })\) is:
(given \(I=\frac{24}{\pi}~\text{kg.m}^2)\) 
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)

7.

The law of conservation of angular momentum is valid when:

1.	The net force is zero and the net torque is non-zero	2.	The net force is non-zero and the net torque is non zero
3.	Net force may or may not be zero and net torque is zero	4.	Both force and torque must be zero

8. Two objects of mass \(10~ \text {kg}\) and \(20~ \text{kg}\) respectively are connected to the two ends of a rigid rod of length \(10~ \text m\) with negligible mass. The distance of the center of mass of the system from the \(10 ~ \text{kg}\) mass is:

1.	\(5~ \text m\)	2.	\(\dfrac{10}{3} \mathrm{~m}\)
3.	\(\dfrac{20}{3} \mathrm{~m}\)	4.	\(10~ \text m\)

9.

The value of \(M\), as shown, for which the rod will be in equilibrium is:
      

1.	\(1\) kg	2.	\(2\) kg
3.	\(4\) kg	4.	\(6\) kg

10.

The moment of inertia of a uniform circular disc of radius '\(R\)' and mass '\(M\)' about an axis touching the disc at its diameter and normal to the disc will be:
1. \(\frac{3}{2} M R^{2}\)
2. \(\frac{1}{2} M R^{2}\)
3. \(M R^{2}\)
4. \(\frac{2}{5} M R^{2}\)${\mathrm{}}^{}$