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Bulk modulus with depth: fractional compression at a depth, or the depth for a given compression

This type of question, asked 5 times: 2021 Paper 8, 2021 Paper 22, 27 Jan 2024, 31 Jan 2024, 29 Jan 2025. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 8

    5
    An object is located at 2 km2\text{ }km beneath the surface of the water. If the fractional compression ΔVV\frac{\Delta V}{V} is 1.36%1.36\%, the ratio of hydraulic stress to the corresponding hydraulic strain will be [Given : density of water is 1000 kg m−31000\text{ }kg{\text{ }m}^{- 3} and g=9.8 ms−2g = 9.8{\text{ }ms}^{- 2}.]

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  2. Question 2

    2021 Paper 22

    21
    When a rubber ball is taken to a depth of ___ m in deep sea, its volume decreases by 0.5%0.5\%. (The bulk modulus of rubber =9.8×108Nm−2= 9.8 \times10^{8}Nm^{- 2} Density of sea water =103kgm−3=10^{3}kgm^{- 3} g=9.8 m/s2g = 9.8\text{ }m/s^{2} )

  3. Question 3

    27 Jan 2024

    30
    If average depth of an ocean is 4000 m4000\text{ }m and the bulk modulus of water is 2×109Nm−22 \times10^{9}Nm^{- 2}, then fractional compression ΔVV\frac{\Delta V}{V} of water at the bottom of ocean is α×10−2\alpha\times10^{- 2}. The value of α\alpha is ____ (Given, g=10 ms−2,ρ=1000 kg m−3g = 10{\text{ }ms}^{- 2},\rho= 1000\text{ }kg{\text{ }m}^{- 3} )

  4. Question 4

    31 Jan 2024

    28
    The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02%0.02\% is  ______m\ \_\_\_\_\_\_ m. (Take density of sea water =103kgm−3=10^{3}kgm^{- 3}, Bulk modulus of rubber =9×108Nm−2= 9 \times10^{8}Nm^{- 2}, and g=10 ms−2g = 10{\text{ }ms}^{- 2} )

  5. Question 5

    29 Jan 2025

    13
    The fractional compression (ΔVV)\left( \frac{\Delta V}{V} \right) of water at the depth of 2.5 km below the sea level is ____\_\_\_\_ %. Given, the Bulk modulus of water =2×109Nm−2= 2 \times10^{9}Nm^{- 2}, density of water =103 kg m−3=10^{3}\text{ }kg{\text{ }m}^{- 3}, acceleration due to gravity =g=10 ms−2= g = 10{\text{ }ms}^{- 2}.

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