A metallic cube of side 8cm is under a tangential force. The top face of the cube is sheared through 0.15 mm with respect to the bottom face. Find (a) shearing stain (b) shearing stress and (c ) shearing force.
Given , modulus of rigidity of the metal
`=2.08 xx 10^(11) dyn e.//cm^(2)` .

Explanation

Here, length of each side of cube L
`8cm`
Lateral displacement , `Delta L = 0.15 mm =0.015cm`
(a) shearing strain, `theta = (Delta L)/(L) = (0.015)/(8)`
`=0.001875`.
(b) Shearing stress = `F/A = G theta`
`(2.08 xx 10^(11)) xx 0.001875`
`=3.9 xx 10^(8) dyn e//cm^(2)`.
(c ) Area of face, `A = 8xx8 cm^(2)`
As `F=F/(A theta) ir F=GA theta`
`:.` Shearing force, `F=GA theta`
`=(2.08 xx 10^(11)) xx (8 xx 8 ) xx 0.001875`
`=0.25 xx 10^(11) dyn e = 2.5 xx 10^(10) dyn e`.