Question

A 0.05 m cube has its upper face displaced by 0.2 cm by a tangential force of 8 N, Calculate the shearing strain, shearing stress and modulus of rigidity of the material of the cube.

Answer 1

$l=5\times {10}^{-2}m,\Delta l=0.2cm=0.2\times {10}^{-2}m,F=8N$
$Shearingstrain=\frac{\Delta l}{l}=\frac{0.2}{5}=0.04$
$Shearingstress=\frac{F}{l\times l}=\frac{8}{(5\times {10}^{-2}{)}^2}=3200N{m}^{-2}$
Modulus of rigidity,

$\eta =\frac{Shearingstress}{Shearingstrain}=\frac{3200}{0.04}=80000N{m}^{-2}=8\times l{0}^{4}N{m}^{-2}$