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Question

Physics Question on Units and measurement

The dimension of the modulus of rigidity, is

A

[ML−2T−2]\left[ ML ^{-2} T ^{-2}\right]

B

[MLT−2]\left[ MLT ^{-2}\right]

C

[ML−1T−1]\left[ ML ^{-1} T ^{-1}\right]

D

[ML−1T−2]\left[ ML ^{-1} T ^{-2}\right]

Answer

[ML−1T−2]\left[ ML ^{-1} T ^{-2}\right]

Explanation

Solution

The modulus of rigidity (η)= Shearing stress  Shearing strain (\eta)=\frac{\text { Shearing stress }}{\text { Shearing strain }} =F/Aϕ=[MLT−2][L2]=\frac{F / A}{\phi}=\frac{\left[ MLT ^{-2}\right]}{\left[ L ^{2}\right]} =[ML−1T−2]=\left[ ML ^{-1} T ^{-2}\right]