Question

A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance at 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 $

Answer 1

Answer: (D)

If radius of gyration is $K$ ,
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 $