$A$ solid sphere is rolling on a surface as shown in the figure,with a translational velocity $v \, ms^{-1}$. If it is to climb the inclined surface continuing to roll without slipping,then the minimum velocity for this to happen is:

$A$ solid sphere is rolling down an inclined plane without slipping. The ratio of its rotational kinetic energy to its total kinetic energy is:

$A$ solid sphere rolls down without slipping on an inclined plane,then the percentage of rotational kinetic energy of the total energy will be ........ $\%.$

$A$ solid sphere of mass $M$ and radius $R$ is rolling down an inclined plane of length $L$ and height $h$ without slipping. What will be the velocity of its center of mass upon reaching the bottom?

$A$ cylinder of mass $10 \; kg$ and radius $15 \; cm$ is rolling perfectly on a plane of inclination $30^{\circ}$. The coefficient of static friction $\mu_{S} = 0.25$.
$(a)$ How much is the force of friction acting on the cylinder?
$(b)$ What is the work done against friction during rolling?
$(c)$ If the inclination $\theta$ of the plane is increased,at what value of $\theta$ does the cylinder begin to skid and not roll perfectly?

$A$ solid sphere and a disc,having the same mass and radius,roll down from rest from the same height on a smooth inclined plane. The ratio of the time taken by them is: