Two uniform thin spherical shells are made from different materials. Both shells have a mass of $2 \,kg$ and an outer radius of $20 \,cm$. When they are both rolled down the same inclined plane without slipping,the times they take to cover equal distances differ by $1 \%$. If the thickness of the thinner shell is $0.5 \,cm$,the thickness of the other one is closest to ........... $\,cm$.

$A$ solid spherical ball rolls on a horizontal surface at $10 \ m \ s^{-1}$ and continues to roll up on an inclined surface as shown in the figure. If the mass of the ball is $11 \ kg$ and frictional losses are negligible, the value of $h$, where the ball stops and starts rolling down the inclination is $($Assume $g = 10 \ m \ s^{-2} )$ (in $m$)

$A$ solid cylinder rolls without slipping down an inclined plane of height $h$. The velocity of the cylinder when it reaches the bottom is

$A$ disc rolls without slipping down an inclined plane of length $L$ and inclination $\theta$. What will be its velocity at the bottom?

$A$ ball rolls down an inclined plane,as shown in the figure. The ball is first released from rest from $P$ and then later from $Q$. Which of the following statement$(s)$ is/are correct?
$(i)$ The ball takes twice as much time to roll from $Q$ to $O$ as it does to roll from $P$ to $O$.
$(ii)$ The acceleration of the ball at $Q$ is twice as large as the acceleration at $P$.
$(iii)$ The ball has twice as much $K.E.$ at $O$ when rolling from $Q$ as it does when rolling from $P$.

$A$ solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$,respectively,then