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Q.

A solid floats in a liquid at $20^{0} C$ with $75 %$ of it immersed. When the liquid is heated to $100^{0} C$ , the same solid floats with $80 %$ of it immersed in the liquid. If the coefficient of expansion of the liquid is $x \times 10^{- 4} /^{\circ} C, then x = . . . . . . . . . . .$ (Assume that the volume of the solid to be constant.)

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answer is 8.47.

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Detailed Solution

In case 1 $m g = \frac{3}{4} [V] \times ρ_{1} g a n d ρ_{1} = d e n s i t y a t 20^{0} C$
In case 2 $m g = \frac{80}{100} [V] ρ_{2} g a n d ρ_{2} = d e n s i t y a t 100^{0} C$
Dividing both the cases $\frac{3}{4} ρ_{1} = \frac{4}{5} ρ_{2}$
$\Rightarrow \frac{3}{4} [\frac{ρ_{0}}{1 + ϒ \times 20}] = \frac{4}{5} [\frac{ρ_{0}}{1 + ϒ \times 100}] \Rightarrow ϒ = 8.47 \times 10^{- 4} /^{0} C$

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