A small sphere of radius R is held against the inner surface of a larger sphere of radius 6R. The masses of large and small spheres are 4M and M, respectively , this arrangement is placed on a horizontal table. There is no friction between any surfaces of contact. The small sphere is now released. Find the coordinates of the centre of the larger sphere when the smaller sphere reaches the other extreme position.

Explanation

Here the horizontal component of `c.m.` is fixed . When the smaller sphere reaches to `B` , the distance traveled by it in the horizontal direction towards the left `= 10 R`.
To balance this , the distance travelled by the (larger + smaller) sphere in the horizontal direction towards the right `= x`.
`M xx 10 R = ( 4 M + M)x`
`x = 2R`
Coordinates of `c.m.` of large sphere `-= (L + 2R , 0)`.