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A cylindrical vessel containing a liquid is closed by a smooth piston of mass m . The area of cross section of the piston is A . If the atmospheric pressure is P0, find the pressure of the liquid just below the piston .?
Most Upvoted Answer
A cylindrical vessel containing a liquid is closed by a smooth piston ...
**Solution:**

To find the pressure of the liquid just below the piston, we need to consider the forces acting on the piston.

1. **Force due to the weight of the piston:**
The weight of the piston is given by the equation:

Weight of the piston (F₁) = mass of the piston (m) * acceleration due to gravity (g)

2. **Force due to the atmospheric pressure:**
The atmospheric pressure (P₀) exerts a force on the entire surface of the piston. The force due to atmospheric pressure is given by the equation:

Force due to atmospheric pressure (F₂) = atmospheric pressure (P₀) * area of cross-section of the piston (A)

3. **Force due to the pressure of the liquid:**
The pressure of the liquid just below the piston exerts a force on the piston. This force is given by the equation:

Force due to liquid pressure (F₃) = pressure of the liquid (P) * area of cross-section of the piston (A)

According to the principle of equilibrium, the net force on the piston should be zero.

So, we can write the equation as:

F₁ + F₂ + F₃ = 0

Substituting the values in the equation, we have:

m * g + P₀ * A + P * A = 0

Simplifying the equation, we get:

P * A = - (m * g + P₀ * A)

Finally, we can express the pressure of the liquid just below the piston (P) as:

P = - (m * g + P₀ * A) / A

Hence, the pressure of the liquid just below the piston is equal to the negative of the sum of the weight of the piston and the atmospheric pressure, divided by the area of the piston.

Note: The negative sign indicates that the pressure of the liquid is acting in the opposite direction to the weight of the piston and the atmospheric pressure.
Community Answer
A cylindrical vessel containing a liquid is closed by a smooth piston ...
Atmospheric pressure plus force (mg) divided by area
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