The dimensions of shear modulus are: [PMT/NEET-2004]
a. $MLT^{-1}$
b. $ML^{2}T^{-2}$
c. $ML^{-1}T^{-2}$
d. $MLT^{-2}$

Answer: Option c — $ML^{-1}T^{-2}$.

Explanation:

• Shear modulus $G$ is defined as the ratio of shear stress to shear strain: $G = \dfrac{\text{shear stress}}{\text{shear strain}}$.
• Shear strain is a pure number (dimensionless).
• Shear stress is force per unit area: $\text{stress} = \dfrac{F}{A}$.
• Force $F = m a$ has dimensions $MLT^{-2}$.
• Area $A$ has dimensions $L^{2}$.
• Therefore, $[\text{stress}] = \dfrac{MLT^{-2}}{L^{2}} = ML^{-1}T^{-2}$.
• Since the denominator (strain) is dimensionless, the shear modulus carries the same dimensions as stress: $ML^{-1}T^{-2}$.