A certain pressure '$\mathrm{P}$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01 \%$ whereas the liquid gets compressed to $0.03 \%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ____________.
Answer (integer)
1
Solution
Given, Volume of water, $V_1=1$ litre
<br/><br/>Volume of liquid, $V_2=2$ litre,
<br/><br/>Pressure $=P$
<br/><br/>$$
\begin{aligned}
& \left(\frac{\Delta V}{V} \times 100\right)_\text { water }=0.01 \% ;\\\\
& \left(\frac{\Delta V}{V} \times 100\right)_\text { liquid }=0.03 \% \\\\
& \text { Bulk modulus, } B=\frac{-P V}{\Delta V} ; \\\\
& \frac{B_{\text {water }}}{B_{\text {liquid }}}=\frac{\left(\frac{\Delta V}{V}\right)_\text { liquid }}{\left(\frac{\Delta V}{V}\right)_\text { water }}=\frac{\frac{0.03}{100}}{\frac{0.01}{100}}=3
\end{aligned}
$$
<br/><br/>On comparing the given value with $\frac{3}{x}$, we get $x=1$.
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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