Three bodies: a ring,a solid cylinder,and a solid sphere,roll down an inclined plane without slipping. They start from rest. Which of the bodies reaches the bottom of the plane with the minimum velocity?

$A$ solid cylinder and a disc of same radii are allowed to roll down a rough inclined plane from the top of a plane. The ratio of their times taken to reach the bottom of the inclined plane is

$A$ disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

$A$ 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 $2M$ and a thin hollow spherical shell of mass $M$ of the same radius roll down an inclined plane simultaneously. Then,

An object of uniform density rolls up a curved path with an initial velocity $v_0$ as shown in the figure. If the maximum height attained by the object is $\frac{7v_0^2}{10g}$ ($g =$ acceleration due to gravity), the object is a . . . . . . .