Verified Solution • 2025–26 Session moderate

QJEEM23Phfe33: JEE Main 2023 Physics - Class 11 JEEM23Phfe33 Solution: A certain pressure ' ' is applied to 1 litre of water and 2…

A certain pressure ' P\mathrm{P} ' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01%0.01 \% whereas the liquid gets compressed to 0.03%0.03 \% . The ratio of Bulk modulus of water to that of the liquid is 3x\frac{3}{x} . The value of xx is ____________.

Step-by-Step Verified Solution

Given, Volume of water, V1=1V_1=1 litre

Volume of liquid, V2=2V_2=2 litre,

Pressure =P=P

amp;(ΔVV×100) water =0.01%;amp;(ΔVV×100) liquid =0.03%amp; Bulk modulus, B=−PVΔV;amp;Bwater Bliquid =(ΔVV) liquid (ΔVV) water =0.031000.01100=3\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}

On comparing the given value with 3x\frac{3}{x} , we get x=1x=1 .

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