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?

1.	Angular acceleration
2.	Angular velocity
3.	Angular displacement in the given time interval
4.	All of these

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 \((\omega)\) about the point \(O,\) then its angular speed about the point \(A\) will be:
                   
1. \(2\omega\)
2. \(\dfrac{\omega}{2}\)
3. \(\omega\)
4. \(\dfrac{\omega}{4}\)

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

               
1. \(\frac{5}{3}mL^2\)
2. \(4mL^2\)
3. \(\frac{1}{4}mL^2\)
4. \(\frac{2}{3}mL^2\)

In the three figures, each wire has a mass M, radius R and a uniform mass distribution. If they form part of a circle of radius R, then about an axis perpendicular to the plane and passing through the centre (shown by crosses), their moment of inertia is in the order:

1.  $I_A$ $>$ $I_B$ $>$ $$ $I_C$

2.  $I_A$ $=$ $I_B$ $=$ $I_C$

3.  $I_A$ $<$ $I_B$ $<$ $I_C$

4.  $I_A$ $<$ $I_C$ $<$ $I_B$

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

Particles \(A\) and \(B\) are separated by \(10~\text m,\) as shown in the figure. If \(A\) is at rest and \(B\) started moving with a speed of \(20~\text{m/s}\) then the angular velocity of \(B\) with respect to \(A\) at that instant is: