The average depth of Indian ocean is about 3000m . The fractional compression, (Δ V/V ) of water at the bottom of the ocean (given that the bulk modulus of the water =2.2× 109 N m- 2 textand g=10 m s- 2 ) is

Question

The average depth of Indian ocean is about 3000m . The fractional compression, (Δ V/V ) of water at the bottom of the ocean (given that the bulk modulus of the water =2.2× 109 N m- 2 textand g=10 m s- 2 ) is (A) 0.82% (B) 0.91% (C) 1.36% (D) 1.52%

Tardigrade Admin · Accepted Answer

The bulk modulus of elasticity is given by

B = \frac{P}{\frac{Δ V}{V}}

So, fractional compression

\frac{Δ V}{V} = \frac{P}{B}

The pressure at the depth

h

in fluid is given as

P = h ρ g

\frac{Δ V}{V} = \frac{ρ g h}{B} \Rightarrow \frac{Δ V}{V} \times 100 = \frac{1000 \times 10 \times 3000}{2.2 \times 1 0 ^{9}} \times 100 = 1.36%

Q. The average depth of Indian ocean is about 3000m . The fractional compression, VΔV​ of water at the bottom of the ocean (given that the bulk modulus of the water =2.2×109Nm−2andg=10ms−2 ) is

0.82%

0.91%

1.36%

1.52%

The bulk modulus of elasticity is given by B=VΔV​P​ So, fractional compression VΔV​=BP​ The pressure at the depth h in fluid is given as P=hρg VΔV​=Bρgh​⇒VΔV​×100=2.2×1091000×10×3000​×100=1.36%

Q. The average depth of Indian ocean is about $3000 m$ . The fractional compression, $\frac{Δ V}{V}$ of water at the bottom of the ocean (given that the bulk modulus of the water $= 2.2 \times 1 0^{9} N m^{- 2} and g = 10 m s^{- 2}$ ) is