$A$ solid cylinder and a solid sphere of same mass and radius roll without slipping on a rough inclined plane. The force of friction is ..........

$A$ horizontal force $F$ is applied at the center of mass of a cylindrical object of mass $m$ and radius $R$,perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $\mu$. The center of mass of the object has an acceleration $a$. The acceleration due to gravity is $g$. Given that the object rolls without slipping,which of the following statement$(s)$ is(are) correct?
$(A)$ For the same $F$,the value of $a$ does not depend on whether the cylinder is solid or hollow
$(B)$ For a solid cylinder,the maximum possible value of $a$ is $2 \mu g$
$(C)$ The magnitude of the frictional force on the object due to the ground is always $\mu m g$
$(D)$ For a thin-walled hollow cylinder,$a = \frac{F}{2m}$

$A$ solid sphere of mass $m$ and radius $r$ rolls down an inclined plane. What is the ratio of its rotational kinetic energy to its translational kinetic energy?

$A$ solid cylinder of mass $m$ and radius $R$ rolls down an inclined plane of height $30 \ m$ without slipping. The speed of its centre of mass when the cylinder reaches the bottom is $[$use $g=10 \ m \ s^{-2}]$ (in $m \ s^{-1}$)

$A$ solid sphere is rolling without slipping on a horizontal rough surface and starts rising on an inclined rough surface as shown in the figure. Assume pure rolling throughout the motion. Choose the $INCORRECT$ statement.

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