Question

Sol. [Key Concept: Solid angle is dimensionless — quantities with same dimensions]

Solid angle $d\Omega = \frac{dA}{r^{2}}$ has dimensions $\left\lbrack M^{0}{\text{ }L}^{0}{\text{ }T}^{0} \right\rbrack$

$$\text{~}\text{Strain}\text{~} = \frac{\Delta l}{l}\text{~}\text{has dimensions}\text{~}\left\lbrack M^{0}{\text{ }L}^{0}{\text{ }T}^{0} \right\rbrack$$

Angle measured in radians is also dimensionless $\left\lbrack M^{0}{\text{ }L}^{0}{\text{ }T}^{0} \right\rbrack$

$$\theta = \frac{l}{r}$$