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A cube has side length 5 cm and modulus of rigidity $$10^5$$ N/m$$^2$$. The displacement produced by a force of 10 N in the upper face of cube is _______ mm.
Correct Answer: 2
Use shear relation:
shear modulus $$G=\frac{\text{stress}}{\text{strain}}$$
$$G=\frac{F/A}{x/L}\Rightarrow x=\frac{FL}{AG}$$
given:
side = 5 cm = 0.05 m
area $$A=(0.05)2=2.5\times10^{-3}m^2$$
L=0.05m
F=10
$$G=10^5$$
$$x=\frac{10\times0.05}{2.5\times10^{-3}\times10^5}$$
$$=\frac{0.5}{250}=0.002m$$
=2 mm
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