Bulk Modulus PYQs: JEE Mains Physics

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1. 1. The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).) 2026 Easy
2. 2. 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. \(\left(\right.\) Take \(\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)\) 2025 Medium
3. 3. The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\). 2025 Medium
4. 4. The increase in pressure required to decrease the volume of a water sample by \(0.2 \%\) is \(\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}\). Bulk modulus of water is \(2.15 \times 10^9 \mathrm{Nm}^{-2}\). The value of P is ________. 2025 Medium
5. 5. The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\), would be ____ \(\mathrm{mm}^3\).
   (Given bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) ) 2025 Easy
6. 6. If average depth of an ocean is \(4000 \mathrm{~m}\) and the bulk modulus of water is \(2 \times 10^9 \mathrm{Nm}^{-2}\), then fractional compression \(\frac{\Delta V}{V}\) of water at the bottom of ocean is \(\alpha \times 10^{-2}\). The value of \(\alpha\) is ___________(Given, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) ) 2024 Hard
7. 7. The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is ______ \(\mathrm{m}\). (Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{Nm}^{-2}\), and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) ) 2024 Hard
8. 8. A certain pressure \(P\) is applied to \(1\) litre of water and \(2\) litre of a liquid separately. Water gets compressed to \(0.01 \%\) whereas the liquid gets compressed to \(0.03 \%\). The ratio of Bulk modulus of water to that of the liquid is \(\frac{3}{x}\). The value of \(x\) is \(...........\) 2023 Medium
9. 9. If \(Y, K\) and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters. 2021 Medium
10. 10. The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of increase in density of material, when a pressure \(P\) is applied uniformly on all sides, will be 2021 Medium
11. 11. A cube of metal is subjected to a hydrostatic pressure of \(4\;GPa.\) The percentage change in the length of the side of the cube is close to.......\(\%\)
    (Given bulk modulus of metal, \(B =8 \times 10^{10}\, Pa\) ) 2020 Medium
12. 12. A solid sphere of radius \(r\) made of a soft material of bulk modulus \(K\) is surrounded by a liquid in a cylindrical container. A massless piston of area \(a\) floats on the surface of the liquid, covering entire crosssection of cylindrical container. When a mass \(m\) is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \(\left( {\frac{{dr}}{r}} \right)\) is  2018 Medium
13. 13. A bottle has an opening of radius \(a\) and length \(b\). A cork of length band radius \(\left( {a + \Delta a} \right)\) where \(\left( {\Delta a <  < a} \right)\) is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is \(B\) and frictional coefficient between the bottle and cork is \(\mu \) then the force needed to push the cork into the bottle is
    2016 Medium
14. 14. The bulk moduli of ethanol, mercury and water are given as \(0.9, 25\) and \(2 .2\) respectively in units of \(10^9\, Nm^{-2}\) . For a given value of pressure, the fractional compression in volume is \(\frac{{\Delta V}}{V}\). Which of the following statements about \(\frac{{\Delta V}}{V}\) for these three liquids is correct ? 2014 Medium

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