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Question

A concrete sphere of radius R has a spherical cavity of radius r which is packed with sawdust. The 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 the mass of sawdust will be

A
8
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B
4
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C
3
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D
1
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Solution

The correct option is B 4

Let V be the volume of the sphere and ρw be the density of the water.
Since sphere is fully submerged under water, then
Weight of whole sphere = Weight of water displaced
(mconcrete+msawdust)g=Vρwg
2.4×43π(R3r3)+0.3×43πr3=43πR3×1
or R3=32r3
mconcretemsawdust=43π(R3r3)ρconcrete43πr3ρsawdust
mconcretemsawdust=2.40.3(32r3r3)r3=4

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