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

A pan containing a layer of uniform thickness of ice is placed on a circular turntable with its centre coinciding with the centre of the turn table. The turntable is now rotated at a constant angular velocity about a vertical axis passing through its centre and then driving is withdrawn. There is no friction between the table. As the ice melts

1.  the angular velocity of the system decreases

2.  the angular velocity of the system increases

3.  the angular velocity of the system remains unchanged

4.  the moment of inertia of the system decreases

The motion of planets in the solar system is an example of the conservation of

1.  mass

2.  Linear momentum

3.  Angular momentum

4.  Energy

Two Circular discs A and B are of equal masses and thicknesses but made of metal with densities ${\mathrm{d}}_{\mathrm{A}} \mathrm{and} {\mathrm{d}}_{\mathrm{B}}$ (${\mathrm{d}}_{\mathrm{A}} > {\mathrm{d}}_{\mathrm{B}}$). If their moments of inertia about an axis passing through their centers and perpendicular to circular faces be ${\mathrm{I}}_{\mathrm{A}} \mathrm{and} {\mathrm{I}}_{\mathrm{B}}$, then

1.  ${\mathrm{I}}_{\mathrm{A}} = {\mathrm{I}}_{\mathrm{B}}$

2.  ${\mathrm{I}}_{\mathrm{A}} > {\mathrm{I}}_{\mathrm{B}}$

3.  ${\mathrm{I}}_{\mathrm{A}}\hspace{0.17em}<\hspace{0.17em}{\mathrm{I}}_{\mathrm{B}}$

4.  ${\mathrm{I}}_{\mathrm{A}} \ge {\mathrm{I}}_{\mathrm{B}}$