QUESTION $8$

Consider the following three objects, each of the same mass and radius:

$(1)$ a solid sphere.

$(2)$ a solid disk.

$(3)$ a hoop

All three are released from rest at the top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. In which order do the objects reach the bottom of the incline?

Hint: Use conservation of energy expressing the angular velocity in terms of the tangential $($translational$)$ velocity. Note that static friction force reyponsible for causing rolling does not do work on the objects as they roll. So static friction work does not feature in energy conservation.

The object with the highest translational velocity reaches the bottom first. At the bottom of the inclined plane, the objects will have both rotational and translational KE$.$

Moment of inertia of the objects are:

$M{R}^2($hoop$),\frac{1}{2}M{R}^2($solid disk$),\frac{2}{5}M{R}^2($solid sphere$)$

A$.1,2,3$

B$.2,3,1$

C$.3,1,2$

D$.3,2,1$