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JEE MAIN 2025
08-04-2025 S2
Question
A sample of a liquid is kept at 1 atm . It is compressed to 5 atm which leads to change of volume of $0.8 \mathrm{~cm}^3$. If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was $\_\_\_\_$ litre. (Take $1 \mathrm{~atm}=10^5 \mathrm{~Pa}$ )
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Solution
Given, Initial pressure of liquid $\left(P_t\right)=1 \mathrm{~atm}$ Final pressure of liquid $\left(\mathrm{P}_{\mathrm{f}}\right)=5 \mathrm{~atm}$ Change in pressure $(d P)=P_f-P_i=4 \mathrm{~atm}$ $$ =4 \times 10^5 \mathrm{~Pa} $$ Change in volume $(\mathrm{dV})=-0.8 \mathrm{~cm}^3$ Bulk modulus $(B)=2 \times 10^9 \mathrm{~Pa}$ Now, $B=\frac{-d P}{(d V / V)} \Rightarrow V=-B\left(\frac{d V}{d P}\right)$ $$ \begin{aligned} & \Rightarrow \mathrm{V}=-2 \times 10^9 \times \frac{\left(-0.8 \times 10^{-6}\right)}{4 \times 10^5} \\ & =4 \times 10^{-3} \mathrm{~m}^3=4 \text { litre } \end{aligned} $$
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