Question

For a wire of length $l$ , maximum change in length under stress condition is $2 \,mm$. What is the charge in length under same conditions when length of wire is halved?

• A. 1 mm
• B. 2 mm
• C. 4 mm
• D. 8 mm

Answer 1

Answer: (A)

1 mm

Answer 2

$Y=\frac{\text { longitudinal stress }}{\text { longitudinal strain }}$ $Y=\frac{F / A}{\Delta V L}$ where $F$ is force, $A$ is area, $\Delta l$ is change is length and $L$ is original length. First case, $Y=\frac{F / A}{2 / L} \ldots$(1) Second case, $Y=\frac{F / A}{\Delta l^{\prime} / L / 2} \ldots$(2) Equating Eqs. (1) and (2), we get $\frac{L}{2} =\frac{L / 2}{\Delta l'}$ $\Rightarrow \Delta l' =1 \,mm$