Home
Class 11
PHYSICS
Find the depth of lake at which density ...

Find the depth of lake at which density of water is `1%` greater than that at the surface. Given compressibility `k= 50 xx10^(-6) atm^(-1)`.

Text Solution

Verified by Experts

`B=(DeltaP)/(-DeltaV//V)implies(DeltaV)/(V)=-(DeltaP)/(B)`
We know `P=P_(atm)+hrhog` and `=rhoV`=constant
`drhoV+dVrho=0implies(drho)/(rho)=-(dV)/(V)i.e., (Deltarho)/(rho)=(DeltaP)/(B)implies(Deltarho)/(rho)=(1)/(100)=(hrhog)/(B)`
[assuming `rho=` constant], `hrhog=(B)/(100)=(1)/(100K)implieshrhog=(1xx1xx10^(5))/(100xx50xx10^(-6))`
`h=(10^(5))/(5000xx10^(-6)xx1000xx10)=(100xx10^(3))/(50)m=2km`
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN|Exercise Exercise 1 (Elasticity)|16 Videos

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN|Exercise Exercise 1 (Surface Tension)|21 Videos

  • CENTRE OF MASS

    ALLEN|Exercise EXERCISE-V B|19 Videos

  • ERROR AND MEASUREMENT

    ALLEN|Exercise Part-2(Exercise-2)(B)|22 Videos

Similar Questions

Explore conceptually related problems

The depth of a lake at which density of water is 2% greater than on surface. [Compressibility of water = 50xx10^(-6) /atm , 1 atm = 10^5N//m^2 ]

Find the depth of a lake at which density of water will be 10% higher than the density at the surface. Compresssibility of water is 0.00005 per atmosphere. Given average density of sea-water =1100 kg m^(-3)

What is the density of ocean water at a depth, where the pressure is 80.0 atm, given that its density at the surface is 1.03 xx 10^(3) kg m^(-3) ? Compressibilty of water = 45.8 xx 10^(-11) Pa^(-1) . Given 1 atm. = 1.013 xx 10^(5) Pa .

Find the depth at which an air bubble of radius 0.7 mm will remain in equilibrium in water . Given surface tension of water = 7.0 xx 10^(-2) N/m.

Compare the densities of water at the surface and bottom of a lake 100 metre deep , given that the compressibility is 10^(-3)//22 per atmosphere and 1 atmosphere = 1.015 xx 10^(5)Pa .

The compressibillity of a gas is greater than unity at 1 atm and 273 K. Therefore :

If the normal density of sea water is 1.00 g//cm^(3) , what will be its density at a depth of 4km? Given compressibility of water = 0.00005 per atmosphere. 1 atmospheric pressure =10^(6) dyn e//cm^(2), g=980 cm//s^(2) .

What is the approximate change in densityof water in a lake at a depth of 400m below the surface ? The density of water at the surface is 1030 kgm^(-3) and bulk modulus of water is 2xx10^(9) Nm^(-2) .

Find the change in density of water in occean at depth of 700m below the surface. The denity of water at the surface is 1000kg//m^(3) and the bulk modulus of water is 4.9xx10^(9) Nm^(-2)