Q87 / 90 · JEE Main 2021 (31 Aug Shift 1) · Physics

When a rubber ball is taken to a depth of _______ $m$ in deep sea, its volume decreases by $0.5 %$
(The bulk modulus of rubber $= 9.8 \times 10^{8} N m^{- 2}$ Density of sea water $= 10^{3} kg m^{- 3}$ , $g = 9.8 m s^{- 2}$ )

Correct answer: 500

Solution

\frac{- d V}{V} = \frac{0.5}{100} = 0.005

B = \frac{- d P}{\frac{d V}{V}} = \frac{ρ g h}{\frac{- d V}{V}}

9.8 \times 10^{8} = \frac{10^{3} \times 9.8 \times h}{5 \times 10^{- 3}} \Rightarrow h = 500 m

Hence, the correct answer is 500.

Relevant Questions

The increase in the pressure required to decrease the volume of water is N/m . The percentage decrease in the volume is _____. (Bulk modulus04 Apr, 2026 (M)Bulk Modulus
A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of . If the bulk modulus of the liquid is 208 Apr, 2025 (E)Bulk Modulus
The fractional compression \( ( { {V}}{ {V}} )\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modul29 Jan, 2025 (M)Bulk Modulus
The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of , would be ____ . (Given bulk28 Jan, 2025 (E)Bulk Modulus
The increase in pressure required to decrease the volume of a water sample by is . Bulk modulus of water is . The value of P is24 Jan, 2025 (E)Bulk Modulus
The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0 . 02 % is _____ m . (Take density of se31 Jan, 2024 (M)Bulk Modulus