The dimensions of shear modulus are

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Accepted Answer

1. **Definition:** Shear modulus (modulus of rigidity) is defined as the ratio of shear stress to shear strain.
2. **Dimensional Analysis:** 
- Shear strain is the ratio of relative displacement to length ($\Delta x / L$), making it a dimensionless quantity $[M^0L^0T^0]$.
- Shear stress is defined as force per unit area ($F/A$). The dimensions of force are $[MLT^{-2}]$ and the dimensions of area are $[L^2]$.
- Therefore, the dimensions of shear stress are $\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.
3. **Conclusion:** Since shear strain is dimensionless, the dimensions of shear modulus are exactly the same as those of shear stress, which is $[ML^{-1}T^{-2}]$.

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