Q119 / 155 · WBJEE 2017 · Physics
A liquid of bulk modulus $k$ is compressed by applying an external pressure such that its density increases by $0.01 \% .$ The pressure applied on the liquid is
- Correct answerA$\frac{k}{10000}$
- B$\frac{k}{1000}$
- C$1000 \mathrm{k}$
- D$0.01 k$
Solution
The Bulk modulus $k$
$$
k=-\frac{p}{\Delta V / V}
$$
Where, $p=$ Pressure
$$
\begin{aligned}
\Delta V &=\text { Change in volume } \\
V &=\text { Volume of liquid }
\end{aligned}
$$
From (i)
$$
\frac{p}{k}=-\frac{\Delta V}{V}=\frac{\Delta p}{p}
$$
$\Rightarrow \quad p=\frac{k \Delta p}{p}$
$$
\begin{aligned}
\Delta p &=0 \cdot 01 \%=0 \cdot 01 / 100 \\
p &=\frac{k}{10000}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.