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

The correct option is D $\sqrt{14}:\sqrt{15}$

Time of descent $t=\frac{1}{\sin \theta }\sqrt{\frac{2h}{g}(1+\frac{k^2}{R^2})}\therefore Ratio=\sqrt{\frac{{(1+\frac{k^2}{R^2})}_{sphere}}{{(1+\frac{k^2}{R^2})}_{disc}}}=\sqrt{\frac{1+\frac{2}{5}}{1+\frac{1}{2}}}=\sqrt{\frac{7}{5}\times \frac{2}{3}}=\sqrt{\frac{14}{15}}$