The average depth of Indian ocean is about 3000 m. The fractional compression, (Δ V/V) of water at the bottom of the ocean is (Given: Bulk modulus of the water = 2.2 Ã 109 N m-2 and g = 10 m s-2)

Question

The average depth of Indian ocean is about 3000 m. The fractional compression, (Δ V/V) of water at the bottom of the ocean is (Given: Bulk modulus of the water = 2.2 Ã 109 N m-2 and g = 10 m s-2) (A) 0.82 % (B) 0.91 % (C) 1.36 % (D) 1.24 %

Tardigrade Admin · Accepted Answer

The pressure exerted by a 3000 m column of water on the bottom layer is

P = h ρ g

= 3000 m \times 1000 k g m^{- 3} \times 10 m s^{- 2}

= 3 \times 1 0^{7} N m^{- 2}

Fractional compression

\frac{Δ V}{V}

is

\frac{Δ V}{V} = \frac{P}{B} = \frac{3 \times 1 0 ^{7} N m ^{- 2}}{2.2 \times 1 0 ^{9} N m ^{- 2}} = 1.36 \times 1 0^{- 2} = 1.36%.

Q. The average depth of Indian ocean is about 3000m. The fractional compression, VΔV​ of water at the bottom of the ocean is (Given : Bulk modulus of the water =2.2×109Nm−2 and g=10ms−2)

0.82 %

0.91 %

1.36 %

1.24 %

The pressure exerted by a 3000 m column of water on the bottom layer is P=hρg =3000m×1000kgm−3×10ms−2 =3×107Nm−2 Fractional compression VΔV​ is VΔV​=BP​=2.2×109Nm−23×107Nm−2​=1.36×10−2=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 is
(Given : Bulk modulus of the water $= 2.2 \times 1 0^{9} N m^{- 2}$ and $g = 10 m s^{- 2}$ )