Q. Two wires of equal cross-section but one made of steel and the other of copper are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. What is the ratio of the lengths of the two wires? (Given : steel = $2 \times 10^{11}Nm^{- 2})$
A) 2 : 11
B) 11 : 2
C) 20 : 11
D) 11 : 20
Explanation
(c) $Y = \frac{stress}{strain}\ \ or\ strain = \frac{stress}{Y}\ or\frac{\mathrm{\Delta}L}{L} = \frac{stress}{Y}\ $
Since, cross-sections are equal and same tension exists in both the wires, therefore, the stresses developed are equal.
Also, $\mathrm{\Delta}L$ is given to be the same for both the wires.
$\therefore\ \ \ L\ \ \propto Y\ $
$\therefore\ \ \frac{L_{s}}{L_{Cu}} = \ \frac{2\ \times 10^{11}}{1.1\ \times 10^{11}} = \frac{20}{11}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.