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Question

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures t1 and t2 of the liquid, fractions f1 and f2 of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

A
f1f2f2t1f1t2
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B
f1f2f1t1f2t2
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C
f1+f2f2t1+f1t2
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D
f1+f2f1t1+f2t2
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Solution

The correct option is A f1f2f2t1f1t2
As with the rise in temperature, the liquid undergoes volume expansion. Therefore the fraction of solid submerged in liquid increases.
Fraction of solid submerged at t1C=f1 Volume of displaced liquid
V0(1+γt1) ...(i)
and fraction of solid submerged at t2C=f2 Volume of displaced liquid
V0(1+γt2) ...(ii)
From Eqs. (i) and (ii), f1f2=1+γt11+γt2
γ=f1f2f2t1f1t2

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