A piece of paraffin wax of density 0.9 g/cc floats on water.A layer of turpentine of density 0.87 g/cc is added on top of water until the wax is entirely submerged.The ratio of the volume of wax immersed in water to that in turpentine is

3 : 13

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87 : 90

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90 : 87

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3 : 10

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Solution

The correct option is D 3 : 10
Buoyant force = weight of liquid displaced
hence $0.9 V = 1 \times V_{1} + 0.87 \times V_{2}$
& $V = V_{1} + V_{2}$
$0.9 (V_{1} + V_{2}) = V_{1} + 0.87 V_{2}$
$0.9 V_{1} + 0.9 V_{2} = V_{1} + 0.87 V_{2}$
$\frac{V_{1}}{V_{2}} = \frac{3}{10}$

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