The approximate depth of an ocean is 2700 , m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given:Depth of ocean,$d = 2700 \, m$Density of water,$ho = 10^3 \, kg/m^3$Compressibility of water,$K = 45.4 	imes 10^{-11} \, Pa^{-1}$Accelera

Vedclass · Accepted Answer

$1.2 	imes 10^{-2}$

Vedclass · Answer

(C) Given:Depth of ocean,$d = 2700 \, m$Density of water,$ho = 10^3 \, kg/m^3$Compressibility of water,$K = 45.4 	imes 10^{-11} \, Pa^{-1}$Acceleration due to gravity,$g = 10 \, m/s^2$The excess pressure at the bottom of the ocean is given by $\Delta P = ho gd$.$\Delta P = 10^3 	imes 10 	imes 2700 = 27 	imes 10^6 \, Pa$.Compressibility $K$ is defined as the reciprocal of the Bulk Modulus $B$,i.e.,$K = \frac{1}{B}$.Since $B = \frac{\Delta P}{(\Delta V/V)}$,we have $\frac{\Delta V}{V} = K 	imes \Delta P$.Substituting the values:$\frac{\Delta V}{V} = (45.4 	imes 10^{-11} \, Pa^{-1}) 	imes (27 	imes 10^6 \, Pa)$$\frac{\Delta V}{V} = 1225.8 	imes 10^{-5} = 1.2258 	imes 10^{-2} \approx 1.2 	imes 10^{-2}$.

The approximate depth of an ocean is $2700 \, m$. The compressibility of water is $45.4 \times 10^{-11} \, Pa^{-1}$ and the density of water is $10^3 \, kg/m^3$. What fractional compression of water will be obtained at the bottom of the ocean?

Similar Questions

If a pressure of $8 \times 10^8 \ N \ m^{-2}$ is applied to a lead block,so that its volume reduces by $20 \%$. The Bulk modulus of the lead block is:

When a pressure of $100 \, atm$ is applied to a rubber ball,its volume decreases by $0.01 \%$. What is the bulk modulus of the rubber?

$A$ glass slab is subjected to a pressure of $10 \, atm$. The fractional change in its volume is (Bulk modulus of glass $= 37 \times 10^9 \, N \, m^{-2}$,$1 \, atm = 1 \times 10^5 \, N \, m^{-2}$)

$A$ ball falling in a lake of depth $200 \ m$ shows $0.1\%$ decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

How much pressure (in atm) is needed to compress a sample of water by $0.4 \%$ (in $\text{ atm}$)? (Assume, Bulk modulus of water $\approx 2.0 \times 10^9 \text{ Pa}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module