Shear Modulus

Shear strain arises when a tangential force is applied parallel to one face of a body while the opposite face is held fixed, causing layers to slide over one another. It is defined as the ratio of the relative horizontal displacement of the top face to the perpendicular distance between the two faces, $\gamma =\frac{\Delta x}{L}$, and equals the small angle of shear in radians. Here the top face shifts by $\Delta x=0.2\text{cm}$ across a cube of height $L=10\text{cm}$, so $\gamma =\frac{0.2}{10}=0.02$. The value 0.002 misplaces a decimal by using 100 cm height. The value 0.2 forgets to divide by the side length. The value 0.0002 introduces an extra factor of one hundred. This definition of shear strain underpins the NCERT introduction of the shear or rigidity modulus $G=\text{shear stress}/\text{shear strain}$, a quantity that is meaningful for solids but effectively zero for fluids, which cannot sustain a static shearing force. Rubber has a notably low rigidity modulus, which is precisely why it deforms so readily under the tangential push described here. As a plausibility check, shear strain is a pure dimensionless ratio, and a value of 0.02 corresponds to a small shear angle of about $1.1^{\circ }$, which is physically reasonable for a modest sideways push on a rubber block.