First slide

Elastic Modulie

Question

Copper of fixed volume V is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is $∆ l .$ Which of the following graphs is a straight line?

Moderate

A

$∆ l versus \frac{1}{l}$
B

$∆ l versus l^{2}$
C

$∆ l versus \frac{1}{l^{2}}$
D

$∆ l versus l$

Solution

Young's modulus Y = $\frac{Stress}{Strain}$
or Y = $\frac{\frac{F}{A}}{\frac{∆ l}{l}} = \frac{Fl}{A ∆ l}$
$\Rightarrow ∆ l = \frac{Fl}{AY}$ -------(i)
The volume of wire V = Al
or A = $\frac{V}{l}$
Substituting the value of A from (ii) in equation (i)
We get $∆ l \infty l^{2}$
Hence the graph of $∆$ l versus $l^{2}$ will give a straight line.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App