A sphere of solid material of specific gravity `8` has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must be

Options

A. `root(3)(3)/(2)`
B. `root(3)(5)/(2)`
C. `root(3)(7)/(2)`
D. `(2)/(root(3)(7))`

Answer

C

Explanation

Weight = upthrust

`((4)/(3)pi R^(3)-(4)/(3) pi r^(3)) (8xxrho_(w)xxg)=((4)/(3)pi R^(3))rho_(w)g`
or `8R^(3)-8r^(3)=R^(3)`
`therefore " " 8r^(3)=7R^(3) " or" (r )/(R )=((7)/(8))^(1//3)=(root(3)7)/(2)`