The volume of the hollow portion of a sphere is 34 of the external volume of the sphere. If it floats in a liquid at relative density 32, half of its external volume immersed, the relative density of the material of the solid is

Let R be external radius of sphere and r be radius of c.Given, 43πr3 = 34(43πR3) ; r3 = 34R3Further, 43π(R3-r3)ρg = 12×43πR3×32ρw×gUsing(i), ρρw = 3

The volume of the hollow portion of a sphere is 34 of the external volume of the sphere. If it floats in a liquid at relative density 32, half of its external volume immersed, the relative density of the material of the solid is

Let R be external radius of sphere and r be radius of c.Given, 43πr3 = 34(43πR3) ; r3 = 34R3Further, 43π(R3-r3)ρg = 12×43πR3×32ρw×gUsing(i), ρρw = 3

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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

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Detailed 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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The volume of the hollow portion of a sphere is 34 of the external volume of the sphere. If it floats in a liquid at relative density 32, half of its external volume immersed, the relative density of the material of the solid is

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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