The bulk modulus of a liquid is $3 \times 10^{10} \mathrm{Nm}^{-2}$. The pressure required to reduce the volume of liquid by $2 \%$ is :

(C) $6 \times 10^{8} \mathrm{Nm}^{-2}$

(A) $3 \times 10^{8} \mathrm{Nm}^{-2}$

(B) $9 \times 10^{8} \mathrm{Nm}^{-2}$

(D) $12 \times 10^{8} \mathrm{Nm}^{-2}$

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Elasticity & SHM

The bulk modulus of a liquid is

3 \times 1 0^{10} Nm^{- 2}

. The pressure required to reduce the volume of liquid by

2%

is :

Answer: (C)

The bulk modulus is defined as

B = \frac{Δ P}{- \frac{Δ V}{V}}

. Given

B = 3 \times 1 0^{10} Nm^{- 2}

and volume reduction

\frac{Δ V}{V} = 0.02

, we have:

Δ P = - B (\frac{Δ V}{V}) = (3 \times 1 0^{10}) (0.02) = 6 \times 1 0^{8} Nm^{- 2}

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option