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The volume of the hollow portion of a sphere is $\frac{3}{4}$ th of the whole volume. It floats in a liquid of relative density 1.5 with half its volume immersed. The relative density of the material of the sphere is

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answer is 3.

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Detailed Solution

Let the volume of the sphere be V. Then the volume of the material of the sphere is $(1 - \frac{3}{4}) V = \frac{1}{4} V$

$If ρ is the relative density of the material, then$

$\frac{1}{4} Vρg = \frac{V}{2} \times 1 .5 ρ \times g$

$\Rightarrow ρ = 3 .0$

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