The moment of inertia of a disc about one of its diameters is:

1.	\(MR^2\)	2.	\(\dfrac{MR^2}{3}\)
3.	\(\dfrac{2MR^2}{3}\)	4.	\(\dfrac{MR^2}{4}\)

The moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end is:

1.  ${\mathrm{Ml}}^2$

2.  $\frac{{\mathrm{Ml}}^2}{2}$

3.  $\frac{{\mathrm{Ml}}^2}{3}$

4.  Can't be determined

Angular velocity at any time \(t\) of a rotating body is given as \(\omega \left(t\right)   =   \omega_{0}   +   \alpha t\). Its magnitude of angular acceleration:

A cord of negligible mass is wound round the rim of a fly wheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord as shown in figure. The flywheel is mounted on a horizontal axle with frictionless bearings. The angular acceleration of the wheel is?

1.   12.5 $\mathrm{rad}/{\mathrm{s}}^2$

2.   10.5 $\mathrm{rad}/{\mathrm{s}}^2$

3.   1.25 $\mathrm{rad}/{\mathrm{s}}^2$

4.   9.25 $\mathrm{rad}/{\mathrm{s}}^2$

A cord of negligible mass is wound round the rim of a flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord as shown in the figure. The flywheel is mounted on a horizontal axle with frictionless bearings. The work done by the pull, when 2m of the cord is unwound is:

1.  20 J

2.  30 J

3.  100 J

4.  50 J

A cord of negligible mass is wound round the rim of a flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord as shown in the figure. The flywheel is mounted on a horizontal axle with frictionless bearings. The kinetic energy of the wheel when 2 m of the cord is unwound? Assume that the wheel starts from rest.

Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

1.   Ring

2.   Solid cylinder

3.   Solid sphere

4.   All bodies will reach the ground with the same speed

From a circular ring of mass \({M}\) and radius \(R,\) an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2.\) The value of \(K\) will be:

A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium?
(Take \(g=10~( \text {m/s}^2)\)