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Q.

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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a

2

b

3

c

2.4

d

1.8

answer is B.

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Detailed Solution

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 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