Bulk modulus of water is 2× 109N/m2 . The change in pressure required to increase the density of water by 0.1 % is

Question

Bulk modulus of water is 2× 109N/m2 . The change in pressure required to increase the density of water by 0.1 % is (A)  2× 109N/m2 (B) 2 × 108 N / m 2 (C) 2 × 106 N / m 2 (D) 2 × 104 N / m 2

Tardigrade Admin · Accepted Answer

Mass = Volume × density =V d= constant V Δ d +d Δ V=0 (Δ V/V) =-(Δ d/d) =-(0.1/100)=10-3 Bulk modulus K=-(Δ p/Δ V / V) Δ p =-K (Δ V/V) Δ p =2 × 109 × 10-3 =2 × 106 N / m 2

Q. 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

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

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

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

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

Mass $=$ Volume $\times$ density $= V d =$ constant
$V Δ d + d Δ V = 0$
$\frac{Δ V}{V} = - \frac{Δ d}{d}$
$= - \frac{0.1}{100} = 1 0^{- 3}$
Bulk modulus $K = - \frac{Δ p}{Δ V / V}$
$Δ p = - K \frac{Δ V}{V}$
$Δ p = 2 \times 1 0^{9} \times 1 0^{- 3}$
$= 2 \times 1 0^{6} N / m^{2}$

Q. Bulk modulus of water is 2×109N/m2 . The change in pressure required to increase the density of water by 0.1% is

2×109N/m2

2×108N/m2

2×106N/m2

2×104N/m2