Question

Pressure is a scalar quantity because
A. It is the ratio of force to area and both force and area are vectors.
B. It is the ratio of the magnitude of the force to area.
C. It is the ratio of the component of the force normal to the area.
D. It depends on the size of the area chosen.

Answer 1

Hint: Physical quantities are divided into scalar and vectors. The quantity having a magnitude and a particular direction is called a vector. The quantity having only magnitude and no specific direction is called a scalar quantity.

Complete step-by-step answer:
In physics, we deal with physical quantities (like speed, distance, time, density, pressure). The physical quantities are divided into scalars and vectors. A scalar is a quantity that has a magnitude, meaning it has a value, which we can measure. A vector is a quantity that has a magnitude and a specific direction, e.g. force.
Pressure is defined as the ratio of the force acting normal to a surface to the area of the surface on which the force is acting. If the force is not normal to the plane of the surface then we take the component normal to the plane into consideration. For example, if a perpendicular force of 10N is acting on a surface of area $5m^2$ then the pressure (P) exerted on it is $P={\displaystyle \frac{\text{perpendicular force}}{\text{area}}}={\displaystyle \frac{10}{5}}=2N{m}^{-2}$.
Now, the question is whether pressure is a scalar quantity or a vector quantity. While calculating only the component of the force that is normal to the surface, on which it is acting, is taken. Therefore, the direction of the original force does not matter. We need to know only the magnitude of the component of the force normal to the surface. Therefore, pressure does not have any specific direction. Hence, it is a scalar quantity.
The correct option is (C) it is the ratio of the component of the force normal to the area.

Note: Since, force and area are both vectors. Sometimes students think that pressure is the ratio of two vectors and therefore they cancel out each other. However, this is a false concept. Why pressure is a scalar quantity is explained in the above section.