$A$ solid sphere,a disc,and a solid cylinder,all of the same mass and made of the same material,are allowed to roll down from rest on an inclined plane. Then,which of the following is true?

$A$ spherical object of mass $M$ and radius $R$ has a moment of inertia $I$ about its axis. If this object rolls down an inclined plane of angle $\theta$ without slipping,its acceleration is given by:

$A$ hollow cylinder and a solid cylinder start rolling down an inclined plane. Which one will take more time to reach the bottom of the plane?

$A$ solid sphere rolls down two different inclined planes of the same height,but of different inclinations. In both cases:

$A$ solid sphere is rolling without slipping on a semi-circular track of radius $R = 10 \ m$ as shown in the figure. The radius of the solid sphere is much smaller than the radius of the semi-circular track. At the lowest point,it has a velocity $v = 10 \ m/s$. To what maximum angle $\theta$ from the vertical will the sphere travel before it comes back down? Neglect the rolling friction between the sphere and the track. (Take $g = 10 \ m/s^2$)

$A$ thick-walled hollow sphere has outside radius $R_0$. It rolls down an incline without slipping and its speed at the bottom is $v_0$. Now the incline is waxed,so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be $5v_0/4$. The radius of gyration of the hollow sphere about an axis through its centre is