Questions

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

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a

71/32

b

51/32

c

91/32

d

31/32

detailed solution

Correct option is A

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

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