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Q.

A sphere of radius R has a concentric cavity o{ radius r. The relative density of the material of the sphere is o. It just floats when placed in a tank full of water. The ratio R/r is

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a

[σ/(σ−1)]1/3

b

[(σ−1)/σ]1/3

c

[σ/(σ−1)]1/2

d

[(σ−1)/σ]1/2

answer is A.

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Detailed Solution

Volume of the sphere =43πR3−r3Now 43πR3−r3σ=43πR3×1or (R/r)=[σ/(σ−1)]1/3
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