Notes : Define Hydrostatic Paradox - Class 11 Physics

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Learn Hydrostatic Paradox Class 11 Physics with easy notes, definition, formula, explanation, diagram, FAQs, MCQs, true/false, fill in the blanks, and exam questions. - Physicskund 

Hydrostatic Paradox

The Hydrostatic Paradox states that the pressure at the same depth in a liquid is the same, irrespective of the shape, size, or volume of the container. Although differently shaped vessels contain different amounts of liquid, the pressure at their bases remains the same if they are filled with the same liquid to the same depth.

Formula

$$P=\rho gh$$

Where,

  • P = Hydrostatic pressure
  • \(\rho\) = Density of the liquid
  • g = Acceleration due to gravity
  • h = Depth of the liquid

Explanation

Consider three vessels A, B, and C of different shapes. They have the same base area and are filled with the same liquid up to the same height. Although each vessel contains a different quantity of liquid, the pressure at the base of every vessel is the same because pressure depends only on density, gravity, and depth. This surprising result is known as the Hydrostatic Paradox.

Why is it Called a Paradox?

Normally, we expect that a larger quantity of water should produce greater pressure. However, even though the vessels contain different amounts of water, the pressure at the base remains the same. This contradiction to common intuition is called a paradox.

Key Points

  • Pressure depends only on density, gravity, and depth.
  • Pressure is independent of the shape of the container.
  • Pressure is independent of the size of the container.
  • Pressure is independent of the volume of liquid.
  • Pressure increases with depth.

Applications

  • Water tanks
  • Dams
  • Hydraulic systems
  • Swimming pools
  • Pressure measuring devices

Frequently Asked Questions (FAQs)

1. What is Hydrostatic Paradox?

Hydrostatic paradox is the phenomenon in which the pressure at the same depth remains the same regardless of the shape or size of the container.

2. Why is it called a paradox?

Because vessels containing different quantities of liquid produce the same pressure at their bases.

3. On what factors does hydrostatic pressure depend?

It depends on the density of the liquid, acceleration due to gravity, and depth.

4. Does hydrostatic pressure depend on the shape of the vessel?

No. It is independent of the shape of the vessel.

5. Which law explains Hydrostatic Paradox?

Pascal's Law together with the hydrostatic pressure equation explains the Hydrostatic Paradox.

Very Short Answer Questions

Q1. State Hydrostatic Paradox.

Answer: Pressure at the same depth is independent of the shape of the container.

Q2. Write the formula for hydrostatic pressure.

Answer:

$$P=\rho gh$$

Q3. What is the SI unit of pressure?

Answer: Pascal (Pa).

Q4. Does hydrostatic pressure depend on the volume of liquid?

Answer: No.

Q5. Which quantity mainly determines hydrostatic pressure?

Answer: Depth of the liquid.

Short Answer Questions

Q1. Explain Hydrostatic Paradox.

Answer:

Hydrostatic paradox states that the pressure at the same depth in a liquid is independent of the shape and size of the container. It depends only on density, gravity, and depth.

Q2. Why do differently shaped vessels exert the same pressure at the base?

Answer:

Because hydrostatic pressure is given by

$$P=\rho gh$$

Since density, gravity, and depth are the same, the pressure at the base is also the same.

Q3. Mention two conditions for Hydrostatic Paradox.

Answer:

  • Same liquid depth.
  • Same liquid density.

Long Answer Question

Explain Hydrostatic Paradox with an example.

Answer:

Consider three vessels of different shapes but having the same base area. They are filled with the same liquid up to the same height. Although each vessel contains a different amount of liquid, the pressure at the bottom of each vessel is equal because

$$P=\rho gh$$

Pressure depends only on density, gravity, and depth and not on the shape or size of the container. This phenomenon is called the Hydrostatic Paradox.

Multiple Choice Questions (MCQs)

1. Hydrostatic pressure depends upon

  • A. Shape of vessel
  • B. Depth of liquid ✅
  • C. Colour of liquid
  • D. Volume of liquid

2. The hydrostatic pressure formula is

  • A. $P=\rho gh$ ✅
  • B. $P=mg$
  • C. $F=ma$
  • D. $PV=nRT$

3. Pressure at the same depth in different vessels is

  • A. Different
  • B. Zero
  • C. Same ✅
  • D. Infinite

4. Hydrostatic pressure does not depend on

  • A. Density
  • B. Gravity
  • C. Depth
  • D. Shape of vessel ✅

5. SI unit of pressure is

  • A. Newton
  • B. Pascal ✅
  • C. Joule
  • D. Watt

True / False

1. Hydrostatic pressure depends on the shape of the vessel. False

2. Pressure at equal depths is equal. True

3. Hydrostatic pressure depends on density. True

4. Different volumes of water always produce different pressures at the same depth. False

5. Pascal is the SI unit of pressure. True

Fill in the Blanks

1. Hydrostatic pressure is given by $\rho gh$.

2. Pressure depends on the depth of the liquid.

3. Pressure is independent of the shape of the container.

4. The SI unit of pressure is Pascal.

5. Hydrostatic pressure increases with increasing depth.

Important Exam Points

  • Hydrostatic pressure depends only on density, gravity, and depth.
  • Pressure is independent of the shape and size of the container.
  • Formula: $P=\rho gh$
  • Hydrostatic paradox is explained by Pascal's Law.
  • Different quantities of liquid can exert the same pressure at equal depths.

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