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JEE Main 2023 (1 Feb, Shift 1) · Bulk Modulus & Compressibility

Bulk Modulus & Compressibility question from JEE Main 2023 (1 Feb, Shift 1)

Q10JEE Main 2023 · 1 FEB · SHIFT 1Medium

Bulk Modulus & Compressibility

A certain pressure 'P\text{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 ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

  1. B=PΔV/VB = \frac{P}{\Delta V/V}; same PP, so B∝1ΔV/VB \propto \frac{1}{\Delta V/V} (the volumes themselves do not matter).
  2. BwBl=0.03%0.01%=3=3x\frac{B_w}{B_l} = \frac{0.03\%}{0.01\%} = 3 = \frac{3}{x}
  3. So x=1x = 1.
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