 # Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. `
Question:

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.

The correct statement for this situation is:-

1. The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.

2. The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.

3. All of them will have same velocity.

4. The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.

Correct Option: 1

Solution:

$\mathrm{a}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^{2}}}$

$\mathrm{I}_{\text {ring }}>\mathrm{I}_{\text {solid cylinder }}>\mathrm{I}_{\text {solid sphere }}$

$\Rightarrow \mathrm{a}_{\text {ring }}<\mathrm{a}_{\text {solid cylinder }}<\mathrm{a}_{\text {solid sphere }}$

$\Rightarrow \mathrm{V}_{\text {ring }}<\mathrm{V}_{\text {solid cylinder }}<\mathrm{V}_{\text {solid sphere }}$