\n\nThe diagram above shows a block under a tangential force producing a shear deformation by angle $\theta$. The shear modulus $G$ is given by
A$G = \dfrac{F/A}{\theta}$
B$G = F \cdot A \cdot \theta$
C$G = \dfrac{\theta}{F/A}$
D$G = \dfrac{F \cdot \theta}{A}$
Answer & Solution
Correct answer: A. $G = \dfrac{F/A}{\theta}$
Shear stress is the tangential force per unit area, $\tau = F/A$. For small angles, shear strain equals the angle of deformation $\theta$ (in radians). Hence $G = \tau / \theta = \dfrac{F/A}{\theta}$.
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