Question

A cube of side $1\text{m}$ fixed at the lower face is acted upon by a tangential force $F$ on its upper surface. If shearing strain is ${10}^{-2}$ due to force $F$, find the distance that the upper face is sheared with respect to lower face.

• A. ${10}^{-3}$ m
• B. ${10}^{-2}$ m
• C. ${10}^{-4}$ m
• D. ${10}^{-1}$ m

Answer 1

The correct option is B ${10}^{-2}$ m



The figure represents the plane, which is showing the shearing action along one of the face of cube.
$F$ is the shearing force acting along the face of cube.
$A{A}^{\prime }=C{C}^{\prime }=x$ is the distance by which face is sheared.
$\Rightarrow \text{Shearing strain}\left(\varphi \right)=\frac{A{A}^{\prime }}{AB}$
Or, $\varphi =\frac{x}{L}$
$\Rightarrow {10}^{-2}=\frac{x}{L}$
$L=1\text{m}$ given
$\therefore x=L\times {10}^{-2}={10}^{-2}\text{m}$