The bulk modulus of water is 2× 109 N m- 2 . The change in pressure required to increase the density of water by 0.1 % is -

Question

The bulk modulus of water is 2× 109 N m- 2 . The change in pressure required to increase the density of water by 0.1 % is - (A) 2× 109 N m- 2 (B) 2× 108 N m- 2 (C) 2× 106 N m- 2 (D) 2× 104 N m- 2

Tardigrade Admin · Accepted Answer

The density would increase by 0.1 % if the volume decrease by 0.1 % , K=(Δ P/(Δ V)V) ⇒ Δ P=K(Δ V/V)=2× 109× (0.1/100)=2× 106 N m- 2

Q. The bulk modulus of water is $2 \times 1 0^{9} N m^{- 2}$ . The change in pressure required to increase the density of water by $0.1%$ is -

$2 \times 1 0^{9} N m^{- 2}$

$2 \times 1 0^{8} N m^{- 2}$

$2 \times 1 0^{6} N m^{- 2}$

$2 \times 1 0^{4} N m^{- 2}$

The density would increase by $0.1%$ if the volume decrease by $0.1%$ ,
$K = \frac{Δ P}{\frac{Δ V}{V}}$
$\Rightarrow Δ P = K \frac{Δ V}{V} = 2 \times 1 0^{9} \times \frac{0.1}{100} = 2 \times 1 0^{6} N m^{- 2}$

Q. The bulk modulus of water is 2×109Nm−2 . The change in pressure required to increase the density of water by 0.1% is -

2×109Nm−2

2×108Nm−2

2×106Nm−2

2×104Nm−2