$A$ solid sphere (mass $2M$) and a thin hollow spherical shell (mass $M$) both of the same size,roll down an inclined plane,then

$A$ disc of mass $m$ and radius $r$ rolls down an inclined plane of height $h$. When it reaches the bottom of the plane,its rotational kinetic energy is ($g=$ acceleration due to gravity).

$A$ 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.

The linear speed of a uniform spherical shell after rolling down an inclined plane of vertical height $h$ from rest is:

$A$ cylinder and a ring of same mass $M$ and radius $R$ are placed on the top of a rough inclined plane of inclination $\theta$. Both are released simultaneously from the same height $h$. Choose the correct statement$(s)$ related to the motion of each body.

$A$ loop rolls down on an inclined plane. The fraction of its total kinetic energy that is associated with the rotational motion is