Question

A tensile force $F$ is applied on all six surfaces of a cube of side unity then increase in length of each side will be ($Y=$ young 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. $\frac{F}{Y(1+2\sigma )}$

Answer 1

Answer: (C)

$\frac{F(1-2\sigma )}{Y}$

$\begin{array}{c}\text{Tensile strain on each face}=\frac{F}{Y}\\ \text{lateral strain due to the other two faces acting}\\ \text{per pendicular}=\frac{-2\sigma F}{Y}\\ \Delta L=(1-2\sigma )\frac{F}{Y}\end{array}$