First slide

Elastic Modulie

Question

When the tension in a metal wire is $T_{1}$ , its length is $l_{1}$ . When the tension is $T_{2}$ , its length is $l_{2}$ .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

$Y = \frac{Fl}{a ∆ l}$
Y, l and a are constants
$∴ \frac{Fl}{∆ l} = constant or ∆ l \propto F$
Now, $l_{1} - l \propto T_{1} and l_{2} - l_{1} \propto T_{2}$
Dividing, $\frac{l_{2} - l}{l_{2} - l} = \frac{T_{1}}{T_{2}}$
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 $l = \frac{l_{2} T_{1} - l_{1} T_{2}}{T_{1} - T_{2}} or l = \frac{l_{1} T_{2} - l_{2} T_{1}}{T_{1} - T_{2}}$

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