What is the relation between energy density and stress? Plot a graph between them.

We know,


Energy space density space equals space 1 half stress cross times strain
or space space Energy space density space equals 1 half stress cross times stress over straight Y
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half fraction numerator left parenthesis stress right parenthesis squared over denominator straight Y end fraction

Graph between Energy density and Stress:

We know,Graph between Energy density and Stress:
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Show that isothermal bulk modulus of a gas is equal to the pressure of the gas.


Bulk modulus is given by,

                   

Negative sign implies if pressure increases volume decreases.

For isothermal condition, equations of state is given by, 

                     PV = constant 

Now, differentiating this equation, we get 



Therefore, bulk modulus of a gas is equal to the pressure of a gas is proved. 
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A cylinder of length l and area of cross section a is filled with liquid of density ρ to a height h. What is the pressure at the bottom due to height column of liquid?

Given, 

Length of the cylinder = 

Area of cross-section = A

Density of the liquid = ρ 

Height of the liquid column = h

Therefore, pressure at the bottom due to height column of liquid is given by, 

                  F = mg

⇒              PA = mg

and,
                 m = ρV = ρhA 

Therefore, P = ρgh

Thus, pressure due to height column of liquid is given by ρgh. 

 
 
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State Pascal’s law.

Pascal's law states that if some pressure is applied at any point of incompressible liquid then the same pressure is transmitted to all the points of liquid and on the walls of the container. 

That is pressure exerted is same in all directions in a fluid at rest.
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You have two identical glass flasks. One is open mouthed and other is filled with helium and sealed. Which of the two will weigh more?

The open mouthed flask will weigh more because the atmospheric particles will get inside the flask which will be obviously heavier than the helium gas. 
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