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Q.

A concrete sphere of radius R has a cavity of a radius r which is packed with sawdust. Specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water.Ratio of mass of concrete to mass of sawdust will be :

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a

4

b

2

c

3.2

d

1.8

answer is A.

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Detailed Solution

For floatation, weight of whole sphere= upthrust43π(R3-r3)ρ1g+43πr3ρ2g=43πR3×ρw×g (R3-r3)ρ1+r3ρ2=R3⇒R3r3=ρ1-ρ2ρ1-1
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