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Physics

Fluid-Mechanics

Easy

Question

The volume of the hollow portion of a sphere is $3 over 4$ of the external volume of the sphere. If it floats in a liquid of relative density $3 over 2$ , half of its external volume immersed, the relative density of the material of the solid is:

2
3
2.4
1.8

The correct answer is: 3

Given, $4 over 3 pi cubed equals 3 over 4 open parentheses 4 over 3 pi R cubed close parentheses semicolon r cubed equals 3 over 4 R cubed$
Further, $4 over 3 pi open parentheses R cubed minus r cubed close parentheses rho g equals 1 half cross times 4 over 3 pi R cubed cross times 3 over 2 rho subscript v cross times g$
Using (i), $rho over rho subscript w equals 3$

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