Given below are two statements:
Statement I : Pressure in a reservoir of water is same at all points at the same level of water.
Statement II : The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correct answer from the options given below :

Question

Two vessels A and B are of the same size and are at the same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. \(P_A\) and \(P_B\) are the pressures of the gases in A and B respectively, then \(\frac{P_A}{P_B}\) is:

Answer 1

To solve the given question, let's evaluate both statements individually based on the principles of fluid mechanics.

Statement I: "Pressure in a reservoir of water is same at all points at the same level of water."
- This statement is true based on Pascal's Law, which states that within a fluid at rest, the pressure exerted at any point is transmitted equally in all directions.
- The pressure at a point in a fluid at rest is given by the formula: P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column above the point.
- This implies that at the same height (or level) in a reservoir of water, the pressure will be constant, assuming the water density is uniform and gravity acts uniformly as well.
Statement II: "The pressure applied to enclosed water is transmitted in all directions equally."
- This statement is also true and is a direct consequence of Pascal's Principle. It states that any change in pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid.
- Pascal's Principle underlies many practical applications such as hydraulic lifts and brakes, where applied pressure is effectively and uniformly transmitted through the hydraulic fluid.

Based on the above explanations, both statements are verified true by the principles of fluid mechanics.

Conclusion: The correct answer is: Both Statement I and Statement II are true.

Answer 2

To solve the given question, let's evaluate both statements individually based on the principles of fluid mechanics.

Statement I: "Pressure in a reservoir of water is same at all points at the same level of water."
- This statement is true based on Pascal's Law, which states that within a fluid at rest, the pressure exerted at any point is transmitted equally in all directions.
- The pressure at a point in a fluid at rest is given by the formula: P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column above the point.
- This implies that at the same height (or level) in a reservoir of water, the pressure will be constant, assuming the water density is uniform and gravity acts uniformly as well.
Statement II: "The pressure applied to enclosed water is transmitted in all directions equally."
- This statement is also true and is a direct consequence of Pascal's Principle. It states that any change in pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid.
- Pascal's Principle underlies many practical applications such as hydraulic lifts and brakes, where applied pressure is effectively and uniformly transmitted through the hydraulic fluid.

Based on the above explanations, both statements are verified true by the principles of fluid mechanics.

Conclusion: The correct answer is: Both Statement I and Statement II are true.

The Correct Option is B

Solution and Explanation

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