An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1/F_2$ is
(1) $\frac{R_2}{R_1}$
(2) $\left(\frac{R_1}{R_2}\right)^2$
(3) 1
(4) $\frac{R_1}{R_2}$

A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v \mathrm{~ms}^{-1}$. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is
(1) $\sqrt{2gh}$
(2) $\sqrt{\frac{7}{5}gh}$
(3) $\sqrt{\frac{7}{2}gh}$
(4) $\sqrt{\frac{10}{7}gh}$

A cord is wound round the circumference of wheel of radius $r$, The axis of the wheel is horizontal and the moment of inertia about it is $I$. A weight $m g$ is attached to the cord at the end. The weight falls from rest. After falling through a distance h , the square of angular velocity of wheel will be
(1) $\frac { 2 m g h } { I + m r ^ { 2 } }$
(2) $\frac { 2 m g h } { I + 2 m r ^ { 2 } }$
(3) $2 g h$
(4) $\frac { 2 g h } { I + m r ^ { 2 } }$

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $h _ { 1 }$ and $h _ { 2 }$, respectively, above the initial level. The ratio $h _ { 1 } : h _ { 2 }$ is $\frac { n } { 10 }$. The value of $n$ is $\_\_\_\_$.