Question

A small sphere of radius R is held against the inner surface if a larger spehere of radius 6R. the masses of large and small spehere are 4M and M respectively. this arrangement is placed ona horixontal table as shown. there is no friction between any surfaces of contact. the small spehere is now released. the coordinates of the centre of the large spehere when thr smaller spehere reaches the other acute extreme positions is

Answer 1

See the diagram.

Radii:  R and 6R.     Masses:  M and 4M.

This is easily solved by the COM Center Of Mass concept.

    There is no external force on the system of the small and big spheres in the horizontal direction. So the center of mass C (horizontal coordinate of COM) remains at the same position.


X coordinate of COM:
        COM C = [ -5R * M + 0 * 4M ] / (M+4 M)
                     = - R

Thus the center of mass is a distance R away from the center of big sphere.

    When the small sphere goes to the other acute extreme, the center of mass C remains at the same position horizontally.  COM will still be at a distance R from the center of big sphere. But on the OTHER Side.

  Then the center of big sphere moves by 2R to the other side of COM. 

The change in the position of large sphere = R - (-R) = 2 R