The average depth of Indian ocean is about 3000 m . The value of fractional compression ((Δ V/V)) of water at the bottom of the ocean is (given that the bulk modulus of water is 2.2 ×109 Nm-2 , g=9.8 , ρH2O=1000 kg.m-3 )

Question

The average depth of Indian ocean is about 3000 m . The value of fractional compression ((Δ V/V)) of water at the bottom of the ocean is (given that the bulk modulus of water is 2.2 ×109 Nm-2 , g=9.8 , ρH2O=1000 kg.m-3 ) (A)  3.4 × 10-2  (B)  1.34 × 10-2  (C)  4.13 × 10-2  (D)  13.4 × 10-2

Tardigrade Admin · Accepted Answer

The fractional compression or decrease in volume

\frac{Δ V}{V} = \frac{h ρ g}{k}

where,

h =

depth (average)

ρ =

density of ocean water

g =

gravitational acceleration and

k =

bulk modulus

\Rightarrow \frac{Δ V}{V} = \frac{3 \times 1 0 ^{3} \times 1 0 ^{3} \times 9.8}{2.2 \times 1 0 ^{9}}

= \frac{3}{2.2} \times 1 0^{- 4} \times 98

= \frac{147}{11} \times 1 0^{- 4} = 1.34 \times 1 0^{- 2}

Q. The average depth of Indian ocean is about $3000 m$ . The value of fractional compression $(\frac{Δ V}{V})$ of water at the bottom of the ocean is (given that the bulk modulus of water is $2.2 \times 1 0^{9} N m^{- 2}$ , $g = 9.8$ , $ρ_{H_{2} O} = 1000 k g . m^{- 3}$ )

$3.4 \times 1 0^{- 2}$

$1.34 \times 1 0^{- 2}$

$4.13 \times 1 0^{- 2}$

$13.4 \times 1 0^{- 2}$

Q. The average depth of Indian ocean is about 3000m . The value of fractional compression (VΔV​) of water at the bottom of the ocean is (given that the bulk modulus of water is 2.2×109Nm−2 , g=9.8 , ρH2​O​=1000kg.m−3 )

3.4×10−2

1.34×10−2

4.13×10−2

13.4×10−2

The fractional compression or decrease in volume VΔV​=khρg​ where, h= depth (average) ρ= density of ocean water g= gravitational acceleration and k= bulk modulus ⇒VΔV​=2.2×1093×103×103×9.8​ =2.23​×10−4×98 =11147​×10−4=1.34×10−2

Q. The average depth of Indian ocean is about $3000 m$ . The value of fractional compression $(\frac{Δ V}{V})$ of water at the bottom of the ocean is (given that the bulk modulus of water is $2.2 \times 1 0^{9} N m^{- 2}$ , $g = 9.8$ , $ρ_{H_{2} O} = 1000 k g . m^{- 3}$ )

$3.4 \times 1 0^{- 2}$

$1.34 \times 1 0^{- 2}$

$4.13 \times 1 0^{- 2}$

$13.4 \times 1 0^{- 2}$