Question

Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodiesare identical. Which of the bodies reaches the round with maximum velocity?

• A. Ring
• B. Solid cylinder
• C. Solid sphere
• D. All reach the ground with same velocity

Answer 1

Answer: (C)

Solid sphere

Answer 2

According to conservation of mechanical energy,

$\mathrm { mgh } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 } \left( 1 + \frac { \mathrm { K } ^ { 2 } } { \mathrm { R } ^ { 2 } } \right)$

or

Note: It is independent of the mass of the rolling body for a ring,

For a solid cylinder,

$\mathrm { v } _ { \mathrm { cylinder } } = \sqrt { \frac { 2 \mathrm { gh } } { 1 + \frac { 1 } { 2 } } } = \sqrt { \frac { 4 \mathrm { gh } } { 3 } }$

For a solid sphere,

Among the given three bodies the solid sphere has the greatest and the ring has the least velocity at the bottom of the inclined plane.