Question

Dimensional formula of stress is
(A) \[{M^0}L{T^{ - 2}}\]
(B) \[{M^0}{L^{ - 1}}{T^{ - 2}}\]
(C) \[M{L^{ - 1}}{T^{ - 2}}\]
(D) \[M{L^2}{T^{ - 2}}\]

Answer 1

Hint: Stress has the same dimension as pressure. The formula for pressure is force exerted on a surface divided by the area of that surface.
Formula used: In this solution we will be using the following formulae;
\[P = \dfrac{F}{A}\] where \[P\] is the pressure exerted on a surface, \[F\] is the force exerted on the surface, and \[A\] is the surface area of that surface.

Complete step by step solution:
We are asked to determine the dimensional formula for stress. To do so, we must note that stress is very similar to pressure and thus have the same dimensional formula, and even in the case of mechanical stress, can be calculated the same way. Hence, we can find the dimensional formula of stress by finding the dimensional formula of pressure.
The formula for calculating pressure in general can be given as
\[P = \dfrac{F}{A}\] where \[P\] is the pressure exerted on a surface, \[F\] is the force exerted on the surface, and \[A\] is the surface area of that surface.
Hence, the dimensional formula can be given as
\[\left[ P \right] = \dfrac{{ML{T^{ - 2}}}}{{{L^2}}}\]
By simplifying the above, we have
\[\left[ P \right] = M{L^{ - 1}}{T^{ - 2}}\] which is the dimensional formula for pressure.
Hence, by equality, it is also the dimensional formula for stress.

Thus, the correct option is C.

Note: For clarity, while pressure is the force applied on a surface per unit area of that surface, stress is actually the force created internally, which resists deformation of a substance per unit area of the substance. Application of pressure on a substance directly causes stress to develop within the substance.