The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances traveled by A and B in the same time interval, then
                          
1. x-2y

2. x = y

3. y=2x

4. none of these

If a gymnast, sitting on a rotating stool, with his arms outstretched, suddenly lowers his hands

1.  the angular velocity increases

2.  his moment of inertia increases

3.  the angular velocity stays constant

4.  the angular momentum increases

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

1.  5 I

2.  3 I

3.  6 I

4.  4 I

A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

1.  Disk

2.   Sphere

3.  Both reach at the same time

4.  Depends on their masses

The rotational KE of a body is E and its moment of inertia is I. The angular momentum is 

1.  EI

2.  $2\sqrt{\left(\mathrm{EI}\right)}$

3.  $\sqrt{\left(2 \mathrm{EI}\right)}$

4.  $\frac{\mathrm{E}}{\mathrm{I}}$

A particle of mass \(m\) moves in the\(XY\) plane with a velocity of \(v\) along the straight line \(AB.\) If the angular momentum of the particle about the origin \(O\) is \(L_A\) when it is at \(A\) and \(L_B\) when it is at \(B,\) then:

If rotational kinetic energy is 50 % of translational kinetic energy, then the body is 

1. Ring

2. Cylinder

3. Hollow sphere

4. Solid sphere

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The centre of mass has an acceleration

1. zero

2. \(\frac{a}{2}\)

3. a

4. 2a

A solid sphere rolls without slipping down a $30°$ inclined plane. If g = 10 $\mathrm{m}/{\mathrm{s}}^2$, the acceleration of the rolling sphere is

1.  5 ${\mathrm{ms}}^{-2}$

2.  $\frac{7}{25}{\mathrm{ms}}^{-2}$

3.  $\frac{25}{7}{\mathrm{ms}}^{-2}$

4.  $\frac{15}{7}{\mathrm{ms}}^{-2}$

If the equation for the displacement of a particle moving on a circular path is given by $\theta =2t^3+0.5$, where $\theta$ is in radian and t is in second, then the angular velocity of the particle after 2s is 

1. 8 rad/s

2. 12 rad/s

3. 24 rad /s

4. 36 rad/s