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 ______ .

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Elasticity & SHM

The increase in pressure required to decrease the volume of a water sample by

0.2%

P \times 1 0^{5} Nm^{- 2}

. Bulk modulus of water is

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

. The value of P is ______ .

Answer: 43

The bulk modulus relates pressure change to fractional volume change:

B = - \frac{Δ P}{Δ V / V} ⟹ Δ P = B (\frac{Δ V}{V})

(taking magnitudes, since the volume decreases under increased pressure).

Here

\frac{Δ V}{V} = 0.2% = 2 \times 1 0^{- 3}

and

B = 2.15 \times 1 0^{9} N/m^{2}

Δ P = 2.15 \times 1 0^{9} \times 2 \times 1 0^{- 3} = 4.3 \times 1 0^{6} N/m^{2} = 43 \times 1 0^{5} N/m^{2} .

P = 43

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Integer answer