Question

The length of a metal wire is $l_{1}$ when the tension in it is $T_{1}$ and is $l_{2}$ when the tension is $T_{2}$ . The natural length of wire is

• A. $\frac{l_{1} + l_{2}}{2}$
• B. $\sqrt{l_{1} l_{2}}$
• C. $\frac{l_{1} T_{2} - l_{2} T_{1}}{T_{2} - T_{1}}$
• D. $\frac{l_{1} T_{2} + l_{2} T_{1}}{T_{2} + T_{1}}$

Answer 1

Answer: (C)

Let the original length be $l$ .
In first case,
$l_{1}=l+dl_{1}$
Using Hooke's law, $x=\frac{T}{K}$
Where, $x$ is the displacement.
We have, $l_{1}=l+\frac{T_{1}}{K}$ ... (i)
Similarly, $l_{2}=l+\frac{T_{2}}{K}$ ... (ii)
Solving Equations. (i) and (ii), we get
$l=\frac{l_{1} T_{2} - l_{2} T_{1}}{T_{2} - T_{1}}$