Question

When a metal wire is stretched by a load, the fractional change in its volume $\left(\frac{\Delta V}{V}\right)$ is proportional to.

• A. $\frac{\Delta l}{l}$
• B. ${\left(\frac{\Delta l}{l}\right)}^2$
• C. $\sqrt{\frac{\Delta l}{l}}$
• D. None of these

Answer 1

Answer: (A)

$\frac{\Delta l}{l}$

By a load, when the metal wire is stretched, in the transverse length, the fractional change is proportional to the longitudinal length's fractional change.

Let the cross functional area be denoted as “$A$” and length is denoted as “l”. Wire's volume is shown as $Al$.

Let's assume that there is no lateral strain when there is an occurrence of longitudinal strain.

Volume increase can be shown as:

$△V=A△l$

$\frac{△V}{V}=\frac{A△l}{Al}=\frac{△l}{l}$

So, $\frac{△V}{V}$ is directly proportional to $\frac{△l}{l}$

Option (A) is correct.