Question

Calculate the ratio of the times taken by a uniform solid sphere and a disc of the same mass and the same diameter to roll down through the same distance from rest on a smooth inclined plane.

• A. $15:14$
• B. $\sqrt{15}:\sqrt{14}$
• C. ${15}^2:{14}^2$
• D. $\sqrt{14}:\sqrt{15}$

Answer 1

Answer: (D)

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

$a=gsin\theta /(R^2+K^2)$

$s=ut+\frac{1}{2}{at}^2$

$u=0$

$s=\frac{1}{2}{at}^2$

$t=\sqrt{\frac{2s}{a}}$

$\frac{t_1}{t_2}=\sqrt{\frac{a_2}{a_1}}$

$a_2=\frac{2}{3}gsin\theta$

$a_1=\frac{5}{7}gsin\theta$

$\sqrt{\frac{\frac{2}{3}gsin\theta }{\frac{5}{7}gsin\theta }}$

$\frac{t_1}{t_2}=\sqrt{\frac{14}{15}}$