A solid sphere of radius R and density r...

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)

the net elongation of the spring is `(4piR^(3)rhog)/(3k)`

the net elongation of theh spring is `(8piR^(3)rhog)/(3k)`

the light sphere is partially submerged

the light sphere is completely submerged.

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The correct Answer is:

A, D

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A sphere of radius R and density rho_1 is dropped in a liquid of density sigma . Its terminal velocity is v_1 . If another sphere of radius R and density rho_2 is dropped in the same liquid, its terminal velocity will be:

`((rho_2-sigma)/(rho_1-sigma))v_1`

`((rho_1-sigma)/(rho_1-sigma))v_1`

`((rho_1)/(rho_2))v_1`

`((rho_2)/(rho_1))v_1`

`(piR^(3)rhog)/(3)`

`(piR^(3)rhog)/(2)`

`piR^(3)rhog`

`(105)/(176) R^(5) rho`

`(176)/(105) R^(5) rho`

`(105)/(176) R^(2) rho`

`(176)/(105) R^(2) rho`