Question

Length of wire becomes 16 cm when certain tension is applied. If the tension is now doubled then wire is further elongated by 1 cm then original length of wire is

• A. 14 cm
• B. 15 cm
• C. 15.5 cm
• D. 16.5 cm

Answer 1

The correct option is B 15 cm

$\text{Let the original length of the wire be}xcm\text{.}$

$\frac{F}{A}=Y\frac{16-x}{x}⟶\left(1\right)$

$\text{if Tension doubles i.e,}2F\text{, final length of wire becomes}17cm\text{.}$

$\begin{array}{c}\frac{2F}{A}=Y\frac{17-x}{x}\to \text{(2)}\\ \text{Using (2)}\&\left(1\right)\\ \frac{2(16-x)}{x}=\frac{17-x}{x}\\ \Rightarrow 32-2x=17-x\\ \Rightarrow 15=x\end{array}$