A metal cube of side 10 cm is subjected to a shearing stress of 106N/m2. Calculate the modulus of rigidity in ×108Nm−2 if the top of the cube is displaced by 0.05 cm with respect to its bottom.

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Detailed Solution

Shearing stress , F/A=106N/m2Length of side, L=10cm=0.1mShearing displacement , Δx=0.05cm=0.0005mThe modulus of rigidity is η=FAθ=FLAΔx∵θ≅tan⁡θ=ΔxL=106×0.10.0005=2×108N/m2

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