$A$ solid sphere and a hollow cylinder roll up without slipping on the same inclined plane with the same initial speed $v$. The sphere and the cylinder reach 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 . . . . . . .

$A$ tennis ball (treated as a hollow spherical shell) starting from $O$ rolls down a hill. At point $A$,the ball becomes airborne,leaving at an angle of $30^\circ$ with the horizontal. The ball strikes the ground at $B$. What is the value of the distance $AB$ (in $m$)? (Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter is $I = \frac{2}{3}mR^2$).

$A$ solid cylinder $P$ rolls without slipping from rest down an inclined plane,attaining a speed $v_p$ at the bottom. Another smooth solid cylinder $Q$ of the same mass and dimensions slides without friction from rest down the inclined plane,attaining a speed $v_q$ at the bottom. The ratio of the speeds $\frac{v_q}{v_p}$ is

$A$ solid cylinder and a solid sphere,having same mass $M$ and radius $R$,roll down the same inclined plane from the top without slipping. They start from rest. The ratio of the velocity of the solid cylinder to that of the solid sphere,with which they reach the ground,will be:

$A$ sphere of mass $2 \, kg$ and radius $0.5 \, m$ is rolling with an initial speed of $1 \, m/s$ up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane,without slipping. How long will the sphere take to return to the starting point $A$? (in seconds)

From an inclined plane,a sphere,a disc,a ring,and a spherical shell of the same radius are rolled without slipping from the same height simultaneously. The order of their reaching at the base will be: