The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height $h$,from rest without sliding,is

$A$ 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 . . . . . . .

Solid cylinders of radii $r_1, r_2$ and $r_3$ roll down an inclined plane from the same place simultaneously. If $r_1 > r_2 > r_3$,which one would reach the bottom first?

$A$ sphere,a disc,a ring,and a hollow sphere of the same radius are rolled down from the same height on an inclined plane simultaneously. The order in which these objects reach the bottom is:

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: $(i)$ a ring of radius $R$,$(ii)$ a solid cylinder of radius $\frac{R}{2}$,and $(iii)$ a solid sphere of radius $\frac{R}{4}$. If,in each case,the speed of the center of mass at the bottom of the incline is the same,the ratio of the maximum heights they climb is:

$A$ ring of radius $4a$ is rigidly fixed in a vertical position on a table. $A$ small disc of mass $m$ and radius $a$ is released as shown in the figure. When the disc rolls down,without slipping,to the lowest point of the ring,then its speed will be