Question

Two bars A and B of circular cross section and of same volume made of same material are subjected to tension, If the diameter of A is half that of B and if the force applied to both the rods is the same and it is in the elastic limit the ratio of extension of A to that of B will be

• A. 16
• B. 8
• C. 4
• D. 2

Answer 1

Answer: (C)

4

$\begin{array}{c}\text{Volume is same,}{V}_1=V_2\\ \text{and}{d}_1=\frac{1}{2}{d}_2\\ \Rightarrow 2d_1=d_2\\ \frac{\pi d_1^2}{\pi d_2^2}=\frac{1}{4}\\ \Rightarrow A_1:A_2=1:4\end{array}$

$\text{Given, Same material and Force}$

$\begin{array}{c}\Delta l=\frac{Fl}{AY}\\ \frac{\Delta l}{l}=\frac{F}{AY}\\ \left(\frac{\Delta l}{l_1}\right)\times \left(\frac{l_2}{\Delta l_2}\right)=\frac{F}{A_{1}Y}\times \frac{A_{2}Y}{F}\\ =4\end{array}$