Q111 / 180 · JIPMER 2015 · Physics
What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of $2.0 \times 10^5 \mathrm{Nm}^{-2}$ from the following data? Density of kerosene $=800 \mathrm{~kg}$ $\mathrm{m}^{-3}$ and speed of sound in kerosene $=1330 \mathrm{~ms}^{-1}$.
- A$0.97 \mathrm{~cm}^{-3}$
- B$0.66 \mathrm{~cm}^{-3}$
- Correct answerC$0.15 \mathrm{~cm}^{-3}$
- D$0.59 \mathrm{~cm}^{-3}$
Solution
As, we know that
$v=\sqrt{\frac{R}{\rho}}$
where, $k=$ bulk modulus of elasticity
$\begin{aligned} \Rightarrow & k & =v^2 \rho=(1330)^2 \times 800 \mathrm{~N} / \mathrm{m}^2 \\ \text { Also, } & k & =\frac{F / A}{\Delta V / V} \\ \Rightarrow & \Delta V & =\frac{\text { pressure }}{k}=\frac{2 \times 10^5}{1330 \times 1330 \times 800} \\ & & =0.15 \mathrm{~cm}^3\end{aligned}$
Hence, the correct answer is option: 'C'.