If average depth of an ocean is 4000 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, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg~m}^{-3}$)

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Elasticity & SHM

If average depth of an ocean is 4000 m and the bulk modulus of water is

2 \times 1 0^{9} Nm^{- 2}

, then fractional compression

\frac{Δ V}{V}

of water at the bottom of ocean is

α \times 1 0^{- 2}

. The value of

α

is ______ (Given,

g = 10 ms^{- 2}, ρ = 1000 kg m^{- 3}

)

Answer: 2

Bulk modulus:

B = - \frac{Δ P}{Δ V / V}

, with

Δ P = ρ g h

the pressure at depth

h

\frac{Δ V}{V} = \frac{ρ g h}{B} = \frac{1000 \times 10 \times 4000}{2 \times 1 0 ^{9}} = 2 \times 1 0^{- 2}

α = 2

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Integer answer