The ratio of the coefficient of volume expansion of a glass...

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 ?

Options

A $2: 5$
B $1: 4$
C $1: 64$
D $1: 8$

Correct answer

B. $1: 4$

Step-by-step solution

When there is no change in liquid level in vessel then

\gamma_{\text{real }}^{\prime}=\gamma^{\prime}

vessel Change in volume in liquid relative to vessel

\Delta \mathrm{V}_{\mathrm{app}}=\mathrm{V} \gamma_{\text{app }}^{\prime} \Delta \theta=\mathrm{V}

\left(\gamma_

{\text{\text{ real } }}

^{\prime}-\gamma_

{\text{\text{ vessel } }}

^{\prime}\right)

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