NEET 2020 Physics Question 167 Solution

When an external deforming force is applied to a body, an internal restoring force per unit cross-sectional area arises to oppose deformation: $$\text{Stress} = \frac{\text{Restoring Force}}{\text{Area}} = \frac{F}{A}$$.

- From Newton's second law $$F = ma$$: $$[F] = [\text{M}] \times [\text{L T}^{-2}] = [\text{M L T}^{-2}]$$ - Area is length squared: $$[A] = [\text{L}] \times [\text{L}] = [\text{L}^2]$$.

$$[\text{Stress}] = \frac{[F]}{[A]} = \frac{[\text{M L T}^{-2}]}{[\text{L}^2]} = [\text{M L}^{1 - 2}\text{T}^{-2}] = [\text{M L}^{-1}\text{T}^{-2}]$$.

Stress has identical dimensions to: - Pressure ($$P = F/A$$) - Young's modulus ($$Y$$ - Bulk modulus ($$B$$ - Modulus of rigidity ($$\eta$$ - Energy density ($$\text{Energy}/\text{Volume}$$ Matches Option 4.