Question

Two bars $A$ and $B$ of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of $A$ is half that of $B$. The ratio of extension of $A$ to $B $ will be:

• A. 16
• B. 2
• C. 1/4
• D. 4

Answer 1

Answer: (A)

$\Delta l=\frac{F L}{\pi r^{2} Y}$
but $V=\pi r^{2} L$
so $L=\frac{V}{\pi r^{2}}=\frac{F V}{\left(\pi r^{2}\right)^{2} Y} \propto \frac{1}{r^{4}}$
$\frac{\Delta l_{A}}{\Delta l_{B}}=\left(\frac{r_{B}}{r_{A}}\right)^{4}=\left(\frac{r_{B}}{r_{B}}{2}\right)^{4}=16$