Question

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In both cases

• A. The speed and time of descend will be same.
• B. The speed will be same but time of descend will be different.
• C. The speed will be different but time of descend will be same.
• D. Speed and time of descend both are different.

Answer 1

Answer: (B)

The speed will be same but time of descend will be different.

Answer 2

Speed of the rolling body at the bottom of inclined plane is.

Where h is the height of the inclined plane, k and R be radius of gyration and radius of the body respectively.

For solid sphere, $\frac { \mathrm { k } ^ { 2 } } { \mathrm { R } ^ { 2 } } = \frac { 2 } { 5 }$

As h is same in both the cases, therefore speed will be same in both cases.

Time of descend,

$\mathrm { t } = \frac { 1 } { \sin \theta } \sqrt { \frac { 2 h } { g } \left( 1 + \frac { k ^ { 2 } } { R ^ { 2 } } \right) }$

Where $\theta$ is angle of k inclination

For solid sphere, $\frac { \mathrm { k } ^ { 2 } } { \mathrm { R } ^ { 2 } } = \frac { 2 } { 5 }$

$\therefore \mathrm { t } = \frac { 1 } { \sin \theta } \sqrt { \frac { 14 \mathrm {~h} } { 5 \mathrm {~g} } }$

As h is same but $\theta$is different in both the cases, hence time of descend will be different in both the cases.