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

Let ρ be the density of the material, ρ0 be the density of water. When the sphere has just started sinking, the weight of the sphere = weight of water displaced (approx.)⇒ 43πR3−r3ρg=43πR3ρ0g⇒ R3−r3ρ=R3ρ0⇒R3−r3R3=ρ0ρ⇒ rR=(7)1/32