The dimensions of shear modulus of rigidity are

The dimensions of shear modulus of rigidity are
  1. \(M^{1} L^{1} T^{-2}\)
  2. \(M^{1} L^{1} T^{-1}\)
  3. \(M L^{2} T^{2}\)
  4. \(M L^{-1} T^{-2}\)

Solution

\(\eta=\frac{\text { tangential stress }}{\text { shearing strain }}=\frac{T}{\theta}=\frac{F / A}{x / L}\)
\(\Rightarrow \quad[\eta]=\frac{M L T^{-2}}{L^{2}}=\left[M L^{-1} T^{-2}\right]\)

Asked in: JEE Mains - Units and Dimensions - Chapter Test

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