A sphere of radius R and made of material of relative density `sigma` has a concentric cavit of radius r. It just floats when placed in a tank full of water. The value of the ratio `R//r` will be

Options

A. ` (sigma )/((sigma - 1 )) `
B. ` ((sigma + 1 ))/(sigma ) `
C. ` ((sigma )/(sigma - 1 )) ^(1//2) `
D. ` ((sigma + 1 )/(sigma )) ^(1//3) `

Answer

C

Explanation

` (4)/(3) pi [ ((D)/(2) ) ^3 - ((d)/(2))^3 ] rho sigma g = (4)/(3) pi ((D)/(2)) ^3 rho g , [ 1 - ((d)/(D))^ 3 ] = (1)/(sigma ) rArr (d)/(D) = ((sigma - 1 ) / (sigma )) ^(1//3) `