A sphere made of a material of specific gravity 8 has a concentric spherical cavity and just sinks in water. Calculate the ratio of the radius of the cavity to that of the outer radius of the sphere.

A sphere made of a material of specific gravity 8 has a concentric sph

1.	A sphere made of a material of specific gravity 8 has a concentric spherical cavity and just sinks in water. Calculate the ratio of the radius of the cavity to that of the outer radius of the sphere.
Answer» SOLUTION :Let the radius of the SPHERE be R and that of the cavity be r. Then, since the sphere just sinks in water, `4/3 pi (R^3 - r^3) rho g = 4/3 pi R^3 rho_w g` `1 - (r/R)^3= (rho_w)/(rho) = 1/8`