Question

A solid sphere and a disc of same mass and radius starts rolling down a rough inclined plane, from the same height the ratio of the time taken in the two cases is

• A. 15 : 14
• B. $\sqrt { 15 } : \sqrt { 14 }$
• C. 14 : 15
• D. $\sqrt { 14 } : \sqrt { 15 }$

Answer 1

Answer: (D)

$\sqrt { 14 } : \sqrt { 15 }$

Answer 2

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

= $= \sqrt { \frac { 1 + \frac { 2 } { 5 } } { 1 + \frac { 1 } { 2 } } }$ $= \sqrt { \frac { 7 } { 5 } \times \frac { 2 } { 3 } } = \sqrt { \frac { 14 } { 15 } }$