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

Answer

A

Explanation

`B=W" " implies(4)/(3)piR^(3) xx 1 xx g =(4)/(3)pi(R^(3)-r^(3))sigma g`
`R^(3)=sigmaR^(3)-sigmar^(3)" "impliessigmar^(3)=(sigma-1)R^(3)" "implies(R )/(r )=((sigma)/(sigma-1))^(1//3)`