Write Pascal's law.

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Q. Write Pascal's law.

Haryana BsehBoard of School Education Haryana (Senior Secondary Part-I / Class 11) 2023Subjective· 2mImportance★★★★★

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Concept understanding — Pascals Principle

Pascal's Principle: The Intuition

Imagine you have a sealed plastic bottle completely filled with water, with no air inside. If you squeeze the bottle at one spot, what happens? The water doesn't just compress at that spot — the entire bottle bulges outward everywhere. The pressure you applied at one point travels instantly through the entire liquid.

That's the core idea: in a confined fluid, pressure applied anywhere is transmitted undiminished to every part of the fluid and to the walls of the container.

Now, why does this happen? Fluids (liquids and gases) are made of particles that can slide past each other. When you push on one part of a confined fluid, those particles bump into their neighbours, which bump into their neighbours, and so on — like a chain of dominoes. Because the fluid is nearly incompressible (especially liquids), the push doesn't get absorbed by squishing the fluid itself. It gets passed along perfectly.

Note

This principle works only for confined fluids — fluids trapped inside a container with no way to escape. An open bucket of water doesn't behave this way because the water can just spill out.

The Precise Statement

P_{\text{applied}} = \frac{F}{A}

In simpler words: if you increase the pressure at one point by $\Delta P$ , every other point in the fluid experiences exactly the same increase $\Delta P$ .

The Key Equation

The pressure $P$ is defined as force per unit area:

P = \frac{F}{A}

So if you apply a force $F_1$ over a small area $A_1$ , you create a pressure $P = F_1/A_1$ . That same pressure pushes on a larger area $A_2$ elsewhere, producing a larger force:

F_2 = P \times A_2 = \frac{F_1}{A_1} \times A_2

This is the force multiplication that makes hydraulic systems work.

Tip

Think of it like this: pressure is the "currency" that gets transferred. Force is what you get when you "cash in" that pressure over a bigger area.

The Classic Example: Hydraulic Lift

A car repair shop uses a hydraulic jack. Here's how it works:

You push down on a small piston (area $A_1 = 10\ \text{cm}^2$ ) with a force of $100\ \text{N}$ .
This creates a pressure $P = 100\ \text{N} / 0.001\ \text{m}^2 = 100,000\ \text{Pa}$ .
That same pressure pushes up on a large piston (area $A_2 = 1000\ \text{cm}^2 = 0.1\ \text{m}^2$ ).
The upward force is $F_2 = P \times A_2 = 100,000 \times 0.1 = 10,000\ \text{N}$ .

You applied $100\ \text{N}$ and got $10,000\ \text{N}$ — a 100× force multiplication. But notice: the small piston moves down 100 cm while the large piston moves up only 1 cm. Work done ( $F \times d$ ) is the same on both sides — you don't get energy for free.

Watch out

Pascal's Principle does not violate energy conservation. Force is multiplied, but distance is divided by the same factor. The product $F \times d$ (work) remains equal.

Where It Applies (and Where It Doesn't)

Applies	Does Not Apply
Hydraulic brakes in cars	Open containers (water in a glass)
Hydraulic jacks and lifts	Gases that are not confined
Dental chairs	Fluids under very high compression (rare)

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Pascal's law: pressure applied anywhere in a confined, incompressible fluid is transmitted equally to every point of the fluid and to the walls of the container, without loss.

Statement: If gravity effects are ignored, the pressure in a fluid at rest is the same at all points; more generally, when an external pressure is applied to an enclosed fluid, that increase in pressure is transmitted undiminished to every point of the fluid and to the walls of the containing vessel, acting perpendicular to the surface at every point.

Mathematically, for an enclosed, incompressible fluid, an applied force $F_1$ over area $A_1$ produces a pressure $P = F_1/A_1$ , and this same pressure $P$ acts at every other point in the fluid, including at a different area $A_2$ , where it produces a force $F_2 = PA_2$ . This gives …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set ANNUAL1 mark
$Q. Hydraulic lift and hydraulic brakes are based on ______ law.$
›Reveal solutionSolution

Hydraulic lifts and hydraulic brakes both work by transmitting pressure equally through an enclosed fluid, which is Pascal's law.

Pascal's law states that a change in pressure applied to an enclosed, incompressible fluid is transmitted undiminished to every point of the fluid and to the walls of its container. In a hydraulic lift/brake, a small force applied on a piston of small cross-sectional area creates a pressure that is transmitted unchanged through the fluid to a piston of larger area, producing …

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CBSE 2026Set ANNUAL1 markMCQ
$Q. Hydraulic lift works on the basis of$
(a) Poiseuille's law
(b) Pascal's law
(c) Archimedes' principle
(d) Bernoulli's principle
›Reveal solutionSolution

Pascal's law states that pressure applied at any point of a confined, incompressible fluid is transmitted undiminished to every other point of the fluid and to the walls of the container -- this is the operating principle of a hydraulic lift.

A hydraulic lift has two pistons of different cross-sectional areas (A1 small, A2 large) connected by an enclosed fluid. A small force F1 applied on the small piston creates a pressure P = F1/A1. By Pascal's law, this same pressure acts on the larger piston:

P = F1/A1 = F2/A2

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. S.I. unit of pressure will be —$
(a) Pascal
(b) Newton
(c) Maxwell
(d) Erg
›Reveal solutionSolution

The SI unit of pressure is the pascal (Pa).

Pressure is defined as $P = \dfrac{F}{A}$ = force per unit area. In SI, force is in newton and area in m², so pressure is in N/m², which is given the special name pascal (Pa).

…

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CBSE 2017Set ANNUAL1 mark
$Q. Write the Pascal's law.$
›Reveal solutionSolution

In an enclosed fluid at rest, a change in pressure applied at one point is transmitted equally to every other point of the fluid and to the container walls.

Pascal's law states that if the pressure at any point in a fluid at rest (in equilibrium, and incompressible) is changed, the change is transmitted without loss to every other point of the fluid and to the walls of the containing vessel, and the pressure at every point acts perpendicular to the surface it touches. This is why a small force applied on a small piston in a hydraulic lift/hydraulic brake produces a much larger force on a larger piston — the pressure P = F/A is the same throughout the connected fluid, so a larger area gives a proportionally larger force (F2 = P × A2). This is the working prin …

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Q.Write Pascal's law.

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