$A$ 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 $m$)

$A$ body is rolling down an inclined plane. If the kinetic energy of rotation is $40\%$ of the translational kinetic energy,then the body is a

An object is rolling on an inclined plane. Its linear and rotational kinetic energies are equal. The object is:

$A$ solid sphere rolls down two different inclined planes of the same heights but different angles of inclination.
$(a)$ Will it reach the bottom with the same speed in each case?
$(b)$ Will it take longer to roll down one plane than the other?
$(c)$ If so,which one and why?

$A$ rolling wheel of $12 \, kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \, kg$ through a string of fixed length and a pulley as shown in the figure. Consider $PR$ as a friction-free surface. The velocity of the centre of mass of the wheel when it reaches the bottom $Q$ of the inclined plane $PQ$ will be $\frac{1}{2} \sqrt{xgh} \, m/s$. The value of $x$ is.............

$A$ solid sphere is thrown up a rough incline. The sphere rolls up without slipping and eventually comes down rolling without slipping. The direction of rolling friction in upward and downward motion respectively is ............