Q. On all the six surfaces of a unit cube, equal tensile force of $F$ is applied. The increase in length of each side will be $(Y =$ Young’s modulus, $\sigma =$ Poisson’s ratio)
A) $\frac{F}{Y(1 - \sigma)}$
B) $\frac{F}{Y(1 + \sigma)}$
C) $\frac{F(1 - 2\sigma)}{Y}$
D) $\frac{F}{Y(1 + 2\sigma)}$
Explanation
(c) Tensile strain on each face $= \frac{F}{Y}$
Lateral strain due to the other two forces acting on perpendicular faces $= \frac{- 2\sigma F}{Y}$
Total increase in length $= (1 - 2\sigma)\frac{F}{Y}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.