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Question

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

A
71/32
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B
51/32
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C
91/32
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D
31/32
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Solution

The correct option is A 71/32
Let ρ be the density of the material. ρo be the density of water. When the sphere has just sunk in water, then

Weight of the sphere = Weight of the water displaced
43π(R3r3)ρsg=43πR3ρwg
(R3r3)ρs=R3ρw(R3r3)R3=ρwρs
1(rR)3=18
rR=71/32

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