$A$ disc of mass $M$ and radius $R$ is rolling on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$,what is the maximum height $h$ reached by the disc?

$A$ uniform solid cylinder of mass $m$ and radius $r$ rolls along an inclined rough plane of inclination $45^{\circ}$. If it starts to roll from rest from the top of the plane,then the linear acceleration of the cylinder axis will be:

$A$ circular ring and a solid sphere having the same radius roll down an inclined plane from rest without slipping. The ratio of their velocities when they reach the bottom of the plane is $\sqrt{\frac{x}{5}}$,where $x=$ . . . . . . .

$A$ solid sphere rolls purely on an inclined plane of inclination $\theta$. Which of the following statements are correct?
$(1)$ The friction force acting on the sphere is $f = \mu mg \cos \theta$.
$(2)$ Friction is a dissipative force.
$(3)$ Friction increases angular velocity and decreases linear velocity.
$(4)$ If $\theta$ decreases,friction decreases.

$A$ cylinder of mass $m$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What will be the velocity of its center of mass when the cylinder reaches the bottom?

$A$ body slides down a smooth inclined plane having angle $\theta$ and reaches the bottom with velocity $v$. If the body is a solid sphere rolling down the same plane,then its linear velocity at the bottom of the plane is