Q. A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance in the same time. If the angle of the plane down which the sphere rolls is $30{^\circ}$. The angle of the other plane is
A) $60{^\circ}$
B) $53{^\circ}$
C) $37{^\circ}$
D) $45{^\circ}$
Explanation
(d) $t = \sqrt{\frac{2l(1 + K^{2}/R^{2})}{g\sin\theta}} = same$
$\therefore\frac{2l(1 + K_{1}^{2} + R^{2})}{g\sin\theta} = \frac{2l(1 + K_{2}^{2}/R^{2})}{g\sin\theta_{2}}$
For sphere, $K_{1}^{2} = \frac{2}{5}R^{2},\ \ \theta_{1} = 30{^\circ}$,
For hollow cylinder, $K_{2}^{2} = R^{2},\ \theta_{2} = ?$
$\frac{1 + \frac{2}{5}}{\sin{30{^\circ}}} = \frac{1 + 1}{\sin\theta_{2}}$
$\sin\theta_{2} = \frac{5}{7} = 0.7143$
$\theta = 45{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.