$A$ solid sphere of mass $0.1\,kg$ and radius $2\,cm$ rolls down an inclined plane $1.4\,m$ in length (slope $1$ in $10$). Starting from rest,its final velocity will be .......... $m/s$.

$A$ solid ball of mass $m$ and radius $r$ rolls without slipping along the track shown in the figure. The radius of the circular part of the track is $R$. The ball starts rolling down the track from rest from a height of $8R$ from the ground level. When the ball reaches the point $P$,then its velocity will be

$A$ 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

$A$ hollow cylinder is rolling on an inclined plane,inclined at an angle of $30^{\circ}$ to the horizontal. Its speed after travelling a distance of $10 \ m$ will be .......... $m/s$.

$A$ disc of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is:

$A$ solid sphere rolls without slipping on an inclined plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is