If P, F and A represent pressure, force and area respectively, then

Question

Accepted Answer

Here's a detailed explanation for the given question:

**Justification for Option 2 (P = F/A) being correct:**

1.  **Definition of Pressure:** Pressure (P) is fundamentally defined as the magnitude of the force (F) applied perpendicular to a surface, divided by the area (A) over which the force is distributed.
2.  **Scalar Nature of Pressure:** Pressure is a scalar quantity. It has magnitude but no specific direction. At any point within a fluid or on a surface, pressure acts equally in all directions.
3.  **Scalar Nature of Force Magnitude and Area:** In the context of this basic definition, 'F' represents the *magnitude* of the force, which is a scalar. 'A' represents the *magnitude* of the area, which is also a scalar.
4.  **Mathematical Consistency:** Therefore, a scalar quantity (Pressure, P) is correctly expressed as the ratio of two other scalar quantities (Force magnitude, F, and Area magnitude, A). The equation $P = \frac{F}{A}$ accurately reflects this definition and the scalar nature of pressure.

**Explanation for why other options are incorrect:**

*   **Option 1: $(P = \frac{\vec{F}}{\vec{A}})$**
    *   **Incorrect Representation of Pressure:** Pressure (P) is a scalar quantity, but this option implies that it is derived from a division of two vectors ($\vec{F}$ and $\vec{A}$).
    *   **Vector Division:** The division of one vector by another vector in this simple form is not a standard mathematical operation that yields a scalar quantity like pressure. While area can be represented as a vector (area vector $\vec{A}$), and force is a vector ($\vec{F}$), their direct division as shown does not define scalar pressure.

*   **Option 3: $(\vec{P} = \frac{\vec{F}}{A})$**
    *   **Incorrect Nature of Pressure:** This option incorrectly represents pressure as a vector quantity ($\vec{P}$). Pressure is a scalar.
    *   **Vector Result:** Dividing a vector ($\vec{F}$) by a scalar (A) results in another vector. Since pressure is a scalar, equating a vector ($\vec{P}$) to a vector ($\frac{\vec{F}}{A}$) is fundamentally incorrect because pressure itself is not a vector.

*   **Option 4: $(P = \frac{\vec{F}}{A})$**
    *   **Scalar Equated to Vector:** This option equates a scalar quantity (Pressure, P) to a vector quantity ($\frac{\vec{F}}{A}$). Dividing a vector ($\vec{F}$) by a scalar (A) yields a vector. A scalar cannot be equal to a vector. This is a fundamental mathematical and physical inconsistency. While the magnitude of the force is used in the pressure calculation, the notation $\vec{F}$ implies the vector quantity, making the equation incorrect for defining scalar pressure.