Analysis of Physics Statements

This question asks us to identify the single correct statement among five options related to physics concepts, specifically focusing on pressure and forces.

Evaluating Statement 1: Pressure's Properties

The first statement claims: "Pressure has magnitude as well as direction".

• Pressure is defined as force per unit area (P = F/A).
• While the force causing pressure acts perpendicularly to a surface (having direction), pressure itself is a scalar quantity.
• A scalar quantity only has magnitude, not direction. For example, atmospheric pressure is the same in all directions at a given point.
• Therefore, this statement is incorrect because pressure is scalar.

Evaluating Statement 2: Pressure with Depth

The second statement suggests: "As we go deeper in a liquid, the pressure decreases".

• The pressure within a liquid increases with depth.
• This is because the deeper you go, the greater the weight of the liquid column above exerts force on the area below.
• The formula for hydrostatic pressure is \(P = \rho gh\), where \(\rho\) is the density of the liquid, \(g\) is the acceleration due to gravity, and \(h\) is the depth. This formula clearly shows pressure (\(P\)) increases as depth (\(h\)) increases.
• Therefore, this statement is incorrect.

Evaluating Statement 3: Action and Reaction Forces

The third statement asserts: "Action and reaction forces act on the same object".

• This statement contradicts Newton's third law of motion.
• Newton's third law states that for every action, there is an equal and opposite reaction.
• Crucially, these action and reaction forces act on different objects. For example, if you push a wall (action on the wall), the wall pushes back on you (reaction on you). The forces are on separate objects.
• Therefore, this statement is incorrect.

Evaluating Statement 4: Unit Equivalence

The fourth statement proposes: "Pascal and N/m\(^2\) represent the same unit".

• The SI unit of pressure is the Pascal, abbreviated as 'Pa'.
• It is defined as the pressure exerted when a force of one Newton (\(N\)) is applied perpendicular to an area of one square meter (\(m^2\)).
• Mathematically, \(1 \text{ Pa} = 1 \text{ N/m}^2\).
• Thus, the Pascal and N/m\(^2\) are indeed equivalent units representing the same physical quantity: pressure.
• Therefore, this statement is correct.

Conclusion

Based on the analysis of each statement, the only correct statement is that the Pascal and N/m\(^2\) represent the same unit of pressure.