The increase in the pressure required to decrease the volume ($\Delta V$) of water is $6.3 \times 10^{7} \text{ N/m}^{2}$. The percentage decrease in the volume is ______. (Bulk modulus of water $= 2.1 \times 10^{9} \text{ N/m}^{2}$.)

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Elasticity & SHM

The increase in the pressure required to decrease the volume (

Δ V

) of water is

6.3 \times 1 0^{7} N/m^{2}

. The percentage decrease in the volume is ______.
(Bulk modulus of water

= 2.1 \times 1 0^{9} N/m^{2}

Answer: (B)

The bulk modulus is

β = - \frac{Δ P}{Δ V / V}

, so the fractional change in volume is

\frac{Δ V}{V} = \frac{Δ P}{β} = \frac{6.3 \times 1 0 ^{7}}{2.1 \times 1 0 ^{9}} = 0.03

. The volume therefore decreases by

3%

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Single correct option