Question

A body of radius R and mass m is rolling horizontally without slipping with speed v. It then rolls up a hill to a maximum height h = . The body might be a -

• A. Solid sphere
• B. Hollow sphere
• C. Disc
• D. Ring

Answer 1

Answer: (C)

Disc

Answer 2

Let I bt the moment of inertia of the body. Then total KE = $\frac { 1 } { 2 }$ mv² + $\frac { 1 } { 2 }$Iw²

or KE = $\frac { 1 } { 2 }$ mv² + $\frac { 1 } { 2 }$I $\left( \omega = \frac { v } { R } \right)$

According to energy conservation loss in KE = gain in PE.

or $\frac { 1 } { 2 }$ $\left( \mathrm { m } + \frac { \mathrm { I } } { \mathrm { R } ^ { 2 } } \right)$ v² = mgh = mg $\left( \frac { 3 v ^ { 2 } } { 4 g } \right)$

Solving this, we get I = $\frac { 1 } { 2 }$ mR²

i.e., the solid body is a disc