Moment of inertia of a uniform cylinder of mass M, radius R and length l about an axis passing through its center and normal to its axis would be

1.  $\frac{{\mathrm{Ml}}^2}{12}$

2.  $\frac{{\mathrm{MR}}^2}{2}$

3.  $\mathrm{M}\left[\frac{{\mathrm{l}}^2}{12}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\frac{{\mathrm{R}}^2}{4}\right]$

4.  $\mathrm{M}\left[\frac{{\mathrm{l}}^2}{12}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\frac{{\mathrm{R}}^2}{2}\right]$

A particle moves along a circle of radius $\frac{20}{\mathrm{\pi }}m$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is

1. 640 $\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$

2. 160 $\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$

3. 40 $\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$

4. 40 $\mathrm{m}/{\mathrm{s}}^2$

If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:

If a force acts on a body at a point away from the centre-of-mass, then:

A sphere can not roll on:

1.  a smooth horizontal surface 

2.  a rough horizontal surface 

3.  a smooth inclined surface 

4.  a rough inclined surface 

Two balls are thrown simultaneously in the air. The acceleration of the centre-of-mass of the two balls while in the air:

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizotal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

1. $\sqrt{\frac{2gh}{I+mr}}$

2. $\sqrt{\frac{2mgh}{I+m{r}^2}}$

3. ${\left[\frac{2mgh}{I+2m}\right]}^{\frac{1}{2}}$

4. $\sqrt{2gh}$

If a person standing on a rotating disc stretches out his hands, the angular speed will

1.  increase

2.  decrease

3.  remain same

4.  None of these

If the earth were to suddenly contract to $\frac{1}{n}$th of its present size without any change in its mass, the duration of the new day will be nearly

1.  24/n hours

2.  24 n hours

3.  24/${\mathrm{n}}^2$ hours

4.   24 ${\mathrm{n}}^2$ hours