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Question

A metallic sphere floats in an immiscible mixture of water and a liquid such that its 45th volume is in water and 15th volume is in the liquid. Then, density of the metal is


A
3.5×103 kg/m3
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B
1.5×103 kg/m3
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C
4×103 kg/m3
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D
2×103 kg/m3
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Solution

The correct option is A 3.5×103 kg/m3
From Archimede's principle,
Total Buoyant force=Weight of displaced fluid
This buoyant force will balance weight of the sphere
Weight of the ball=Weight of displaced fluid
Buoyant force due to immersion in both liquids will balance the weight of sphere.
ρmetalgV=ρwg×(45V)+ρLg×(15V)
[For sphere, W=mg=ρmetalgV]
ρmetal=45ρw+15ρL
Substituting the given data,
ρmetal=45×103+15×13.5×103
ρmetal=3.5×103 kg/m3

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