The average depth of Indian ocean is about 5000 m. What will be the percentage fractional compression of water at the bottom of the ocean, given that the bulk modulus of water is 3 × 109 Pa ⋅ g =9.8 m / s 2 (1 Pa =1 N / m 2)

Question

The average depth of Indian ocean is about 5000 m. What will be the percentage fractional compression of water at the bottom of the ocean, given that the bulk modulus of water is 3 × 109 Pa ⋅ g =9.8 m / s 2 (1 Pa =1 N / m 2) (A) 17 % (B) 1.6 % (C) 19 % (D) 18 %

Tardigrade Admin · Accepted Answer

P=h ρ g=5000 × 103 × 9.8 ∴ B=(P/Δ V) × V ⇒ (Δ V/V) =(P/B)=(5000 × 103 × 9.8/3 × 109) ∴ (Δ V/V)=16333.3 × 10-6=1.6 × 10-2 (Δ V/V) × 100=1.6 %

Q. The average depth of Indian ocean is about $5000 m$ . What will be the percentage fractional compression of water at the bottom of the ocean, given that the bulk modulus of water is $3 \times 1 0^{9} P a \cdot g = 9.8 m / s^{2}$
$(1 P a = 1 N / m^{2})$

$17%$

$1.6%$

$19%$

$18%$

$P = h ρ g = 5000 \times 1 0^{3} \times 9.8$
$∴ B = \frac{P}{Δ V} \times V$
$\Rightarrow \frac{Δ V}{V}$
$= \frac{P}{B} = \frac{5000 \times 1 0 ^{3} \times 9.8}{3 \times 1 0 ^{9}}$
$∴ \frac{Δ V}{V} = 16333.3 \times 1 0^{- 6} = 1.6 \times 1 0^{- 2}$
$\frac{Δ V}{V} \times 100 = 1.6%$

Q. The average depth of Indian ocean is about 5000m. What will be the percentage fractional compression of water at the bottom of the ocean, given that the bulk modulus of water is 3×109Pa⋅g=9.8m/s2 (1Pa=1N/m2)

17%

1.6%

19%

18%