A uniform sphere of mass m and radius r rolls without slipping down a inclined plane, inclined at an angle `45^(@)` to the horizontal . Find the magnitude of frictional coefficient at which slipping is absent :

Options

A. The sphere will always roll without slipping
B. The sphere will always slide
C. The sphere will roll without slipping only if `theta le "sin" (7 mu)/(2)`
D. The sphere will roll without slipping only if `theta le "tan"^(-1) (7mu)/(2)`

Answer

D

Explanation

`mu ge (tan theta)/(1+ (MR^(2))/(I)) rArr mu ge (tan theta)/(1+ (5)/(2)) rArr theta le tan^(-1) ((7 mu)/(2))`