Question

When a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to
(a) ∆ll
(b) (∆ll)2
(c) √∆l/l
(d) none of these

Answer 1

Answer:

(a) ∆||..

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Answer 2

The fractional change in its volume is proportional to $\frac{\Delta l}{1}.$

Explanation:

• 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:

$\Delta V=A \Delta l$

  $\frac{\Delta V}{V}=\frac{A \Delta l}{A l}=\frac{\Delta l}{l}$

So,  $\frac{\Delta V}{V}$ is directly proportional to $\frac{\Delta t}{t}$.