A wheel is rotating at the rate of 33 rev/min.  If it comes to stop in 20 s. Then, the angular retardation will be

1. $\mathrm{\pi }\frac{\mathrm{rad}}{{\mathrm{s}}^2}$                         

2. $11\mathrm{\pi } \mathrm{rad}/{\mathrm{s}}^2$

3. $\frac{\mathrm{\pi }}{200} rad/s^2$             

4. $\frac{11\mathrm{\pi }}{200} rad/s^2$

A solid sphere is rotating about a diameter at an angular velocity $\omega$.  If it cools so that its radius reduces to $\frac{1}{n}$ of its  original value, its angular velocity becomes [MP PMT 2006]

1. $\frac{\omega }{n}$                                2. $\frac{\omega }{n^2}$

3. $n\omega$                               4. $n^2\omega$

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

1. Decreases continuously

2. Decreases initially and increases again

3. Remains unaltered

4. Increases continuously

For L = 3.0 m, the total torque about pivot A provided by the forces as shown in the figure is:

For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?

1. A disc of radius a

2. a ring of radius a

3. a square lamina of side 2 a

4. four rods forming square of side 2 a.

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is

1. $\frac{L}{2\sqrt{3}}$

2. $\frac{L^2}{12}$

3. $\frac{L}{\sqrt{3}}$

4. $\frac{L}{\sqrt{2}}$

Two uniform, thin, identical rods, each of mass M and length l are joined together to form a cross. What will be the moment of inertia of the cross about an axis passing through the point at which the two rods are joined and are perpendicular to the plane of the cross?

1. $\frac{M{l}^2}{12}$

2. $\frac{M{l}^2}{6}$

3. $\frac{M{l}^2}{4}$

4. $\frac{M{l}^2}{3}$

If the linear momentum is increased by 50%, the kinetic energy will increase by

1.  50%

2.  100%

3.  125%

4.  25%

If the kinetic energy of a body increases by 0.1%, the percent increase of its momentum will be 

1.  0.05%

2.  0.1%

3.  1.0%

4.  10%

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

1.  Both together only when the angle of inclination of the plane is ${45}^0$

2.  Both together

3.  Hollow cylinder

4.  Solid cylinder