Question

A solid sphere and a spherical shell roll down on inclined plane from rest from same height.The ratio of the times taken by them is.

• A. $\sqrt{\frac{21}{25}}$
• B. 21/25
• C. $\sqrt{\frac{25}{21}}$
• D. 25/21

Answer 1

The correct option is A $\sqrt{\frac{21}{25}}$

Acceleration $a=\frac{9\sin \theta }{1+\frac{I}{m{R}^2}}$; $\theta =$ inclination

Time $t=\sqrt{\frac{2s}{a}}$; $s=$ length of incline

$\Rightarrow t=\sqrt{\frac{2s(1+\frac{I}{m{R}^2})}{9\sin \theta }}$

$\Rightarrow \frac{t_{s^o}}{t_{s_n}}=\sqrt{\frac{1+\frac{2}{5}\frac{m{R}^2}{m{R}^2}}{1+\frac{2}{3}\frac{m{R}^2}{m{R}^2}}}$

or $\frac{t_{so}}{t_{sn}}=\sqrt{\frac{7\times 3}{5\times 5}}=\sqrt{\frac{21}{25}}$.