First slide

Fluid statics

Question

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

Moderate

A

2
B

3
C

2.4
D

1.8

Solution

Let R be external radius of sphere and r be radius of c.
Given, $\frac{4}{3} {πr}^{3} = \frac{3}{4} (\frac{4}{3} {πR}^{3}); r^{3} = \frac{3}{4} R^{3}$
Further, $\frac{4}{3} π (R^{3} - r^{3}) ρg = \frac{1}{2} \times \frac{4}{3} {πR}^{3} \times \frac{3}{2} ρ_{w} \times g$
Using(i), $\frac{ρ}{ρ_{w}} = 3$

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