A solid sphere of radius R and density `rho` is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density `3rho`. The complete arrangement is placed in a liquid of density `2rho` and is allowed to reach equilibrium. The correct statements(s) is (are)

Options

A. the net elongation of the spring is `(4piR^(3)rhog)/(3k)`
B. the net elongation of th spring is `(8piR^(3)rhog)/(3k)`
C. the light sphere is partially submerged.
D. the light sphere is completely submerged.

Answer

A, D

Explanation

On small sphere
`(4)/(3)piR^(3)(rho)g + kx = (4)/(3)piR^(3)(2rho)g …(i)`
on second sphere
`(4)/(3)piR^(3)(3rho)g = (4)/(3)piR^(3)(2rho)g + kx ….(ii)`
by equation `(i)` and `(ii)`
`x = (4piR^(3)rhog)/(3k)`