Mechanical Properties of Solids

JEE Main level, numerical answer, medium

93 of 118

Question 93 of 118

A certain pressure 'PP' is applied to 11 litre of water and 22 litre of a liquid separately. Water gets compressed to 0.010.01% whereas the liquid gets compressed to 0.030.03%. The ratio of Bulk modulus of water to that of the liquid is 3x\dfrac{3}{x}. The value of xx is ______.

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Answer: 1

Bulk modulus is given by B=−ΔP(ΔVV)B=\dfrac{-\Delta P}{\left(\dfrac{\Delta V}{V}\right)}
Now, in case of water, Bwater=−ΔP(ΔVV)=−ΔP0.01100{B}_{water}=\dfrac{-\Delta P}{\left(\dfrac{\Delta V}{V}\right)}=\dfrac{-\Delta P}{\dfrac{0.01}{100}}
In case of liquid, Bliquid=−ΔP0.03100{B}_{liquid}=\dfrac{-\Delta P}{\dfrac{0.03}{100}}
Thus, the ratio BwaterBliquid=−ΔP0.0001−ΔP0.0003=3\dfrac{{B}_{water}}{{B}_{liquid}}=\dfrac{\dfrac{-\Delta P}{0.0001}}{\dfrac{-\Delta P}{0.0003}}=3
Hence, the value of x=1x=1.

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