Question

What is the relationship between pressure and the area of contact?

Answer 1

Hint: Study about how pressure is applied on a body. Obtain the expression for pressure and try to define how pressure is dependent on which quantity. Find the relation between pressure and the area of contact of the body.

Complete step by step answer:
Pressure on an object can be defined as the physical force exerted on the object. Pressure can be defined as the force applied perpendicular to the surface of an object per unit area of that surface. Pressure can be mathematically expressed as,
$\text{pressure = }\dfrac{\text{force applied}}{\text{area of contact}}$
$\text{or, P=}\dfrac{F}{A}$
Where p is the pressure on the object, F is the force applied on the object and A is the area of contact of the force and the surface of the object.
So, we can write,
$p\propto \dfrac{1}{A}$
Hence, pressure is inversely proportional to the area of contact.

Additional information:
In the SI unit system, the unit of force is Newton and the unit of area is square-meter.
So, in SI unit, the unit of pressure will be $N{{m}^{-2}}$
Dimension of pressure will be, $\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]$
Atmospheric pressure can be defined as the pressure given by the atmosphere of earth near the surface or at sea level.
Hydrostatic pressure can be defined as the pressure due to fluid on an object at a given depth.
Hydrostatic pressure is expressed as,
$P=\rho gh$
Where, $\rho $ is the density of the fluid, g is the acceleration due to gravity and h is the depth at which the object is in the fluid.

Note: Point forces are independent of area. When we measure pressure on an object we take the perpendicular component of the force to the surface of the body. Pressure is scalar, so it does not have any direction.