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NEET PHYSICSEasy

The dimensions of shear modulus are

A

$MLT^{-1}$

B

$ML^2T^{-2}$

C

$ML^{-1}T^{-2}$

D

$MLT^{-2}$

Step-by-Step Solution

Definition: Shear modulus (modulus of rigidity) is defined as the ratio of shear stress to shear strain.
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 $\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$ .

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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