Question

The ratio of the coefficient of volume expansion of a glass
container to that of a viscous liquid kept inside the container
is 1 : 4. What fraction of the inner volume of the container
should the liquid occupy so that the volume of the remaining
vacant space will be same at all temperatures ?
(a) 2:5 (b) 1:4 (c) 1:64 (d) 1:8​

Answer 1

answer : option (b) 1 : 4

a/c to question, the volume of remaining haven't space will be same at all temperature.

it means, there is no change in volume at all temperature.

it implies that, $\gamma_{real}=\gamma_{vessel}$

so, change in glass container = change in liquid occupied in the container

⇒$V_g\gamma_g\Delta T=V_l\gamma_l\Delta T$

it is given, $\frac{\gamma_g}{\gamma_l}=\frac{1}{4}$

so,$\frac{V_l}{V_g}=\frac{1}{4}$

hence, answer is option (b) 1 : 4

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Answer 2

$\huge\bold\purple{Answer:-}$

(b) 1:4