First slide

Elastic behaviour of solids

Question

When the tension in a metal wire is T₁, its length is l₁. When the tension is T₂, its length is l₂.The natural length of wire is

Moderate

A

$\frac{T_{2}}{T_{1}} (l_{1} + l_{2})$
B

$T_{1} l_{1} + T_{2} l_{2}$
C

$\frac{l_{1} T_{2} - l_{2} T_{1}}{T_{2} - T_{1}}$
D

$\frac{l_{1} T_{2} + l_{2} T_{1}}{T_{2} + T_{1}}$

Solution

$Y = \frac{Fl}{aΔl}$
Y, I and a are constants
$∴ \frac{Fl}{Δl} = constant or Δl \propto F$
$Now, l_{1} - l = T_{1} and l_{2} - l = T_{2}$
$Dividing, \frac{l_{1} - l}{l_{2} - l} = \frac{T_{1}}{T_{2}}$
$\begin{array}{l} or l_{1} T_{2} - {lT}_{2} = l_{2} T_{1} - {lT}_{1} \\ or l (T_{1} - T_{2}) = l_{2} T_{1} - l_{1} T_{2} \\ or l = \frac{l_{2} T_{1} - l_{1} T_{2}}{T_{1} - T_{2}} or l = \frac{l_{1} T_{2} - l_{2} T_{1}}{T_{2} - T_{1}} \end{array}$

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