A solid sphere of radius R and density ` rho ` is attached to end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density ` 3p`. The complete arrangement is placed is a liquid of density and is allowed to reach equilibrium. The correct statement(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)`