Discussion Forum



1)

A solid sphere of radius R and density $\rho$  is attached to one 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 3$\rho$. The complete arrangement is placed in a liquid of density 2$\rho$  and is allowed to reach equilibrium. The correct statement(s) is (are)


A) the net elongation of the spring is $\frac{4\pi R^{3}\rho g}{3k}$

B) the net elongation of the spring is $\frac{8\pi R^{3}\rho g}{3k}$

C) the light sphere is partially submerged

D) the light sphere is completely submeged

Answer:

Option A,D

Explanation:

842021121_m6.JPG

 On small sphere

  $\frac{4}{3}\pi R^{3}(\rho)g+kx=\frac{4}{3}\pi R^{3}(2\rho) g$    ......(i)

  On second sphere (large)

  $\frac{4}{3}\pi R^{3}(3\rho)g=\frac{4}{3}\pi R^{3}(2\rho) g+kx$   .....(ii)

 By Eqs. (i) and (ii) , we get

    x= $\frac{4\pi R^{3}\rho g}{3k}$