# A solid sphere of mass m and radius R is rigidly enclosed in solid hollow shell of same mass m & radius R. This body is rolling down a rough incline of inclination pi/4.If minimum value of coefficient of static friction is x/23. Find value of x?

Feb 2, 2018

$8$

#### Explanation:

Here, $\theta = 45$, and moment of inertia $I = \frac{2}{3} M {r}^{2} + \frac{2}{5} M {r}^{2}$ (hollow sphere+solid sphere) and mass $m = 2 M$
Putting the values,we get, $\mu$ greater or equal $\frac{8}{23}$
So, $\frac{x}{23} = \frac{8}{23}$ or, $x = 8$