The moment of inertia of a horizontal ring about its vertical axis through the centre is mR². The moment of inertia about its tangent parallel to the plane is:

1.  $\frac{3{\mathrm{mR}}^2}{2}$

2.  $\frac{{\mathrm{mR}}^2}{4}$

3.  $\frac{{\mathrm{mR}}^2}{2}$

4.  $\frac{3{\mathrm{mR}}^2}{4}$

A uniform rod of length l is hinged at one end and is free to rotate in the vertical plane. The rod is released from its position, making an angle $\theta$ with the vertical. The acceleration of the free end of the rod at the instant it is released is:
    

On a rough horizontal surface (coefficient of friction $\mu$), a cubical block of side 'a' and mass m is projected horizontally. The net torque on the block about its centre of mass till the block stops is equal to:

1.  zero

2.  $\frac{1}{2}\mu mga$

3.  $\mu$mga

4.  mga

An insect, initially on the circumference of a disc, starts moving along a chord of the disc, rotating about an axis passing through the center and perpendicular to the plane of the disc. Its angular speed: 

For a rigid body rotating about a fixed axis, which of the following quantities is the same at an instant for all the particles of the body?

A body of mass M is moving on a circular track of radius r in such a way that its kinetic energy K depends on the distance travelled by the body s according to relation K = $\beta$s, where $\beta$ is a constant. The angular acceleration of the body is:

1.  $\frac{\beta r}{M^2}$

2.  $\sqrt{\frac{\beta r}{M}}$

3.  $\frac{M{r}^2}{\beta }$

4.  $\frac{\beta }{Mr}$

If a particle moves in a circle with a constant angular speed ($\mathrm{\omega }$) about point O, then its angular speed about point A will be:
           
1.  2$\mathrm{\omega }$

2.  $\frac{\mathrm{\omega }}{2}$

3.  $\mathrm{\omega }$

4.  $\frac{\mathrm{\omega }}{4}$

Which of the following is the value of the torque of force \(F\) about origin \(O:\)

1. \(\vec{\tau}=5(1-\sqrt{3}) \hat{k}\) N-m
2. \(\vec{\tau}=5(1-\sqrt{3}) \hat{j}\) N-m
3. \(\vec{\tau}=5(\sqrt{3}-1) \hat{i}\) N-m
4. \(\vec{\tau}=\sqrt{3} \hat{j}\) N-m

Four thin rods, each of mass m and length L, form a square. The moment of inertia on any side of the square is:

             
1.  $\frac{5}{3}m{L}^2$

2.  $4$ $m{l}^2$

3.  $\frac{m{L}^2}{4}$

4.   $\frac{2}{3}m{L}^2$