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8.Mechanical Properties of Solids
easy
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 $\Delta l$. Which of the following graphs is a straight line?
A
$\Delta l \rightarrow \frac {1}{l}$
B
$\Delta l \rightarrow l^2$
C
$ \Delta l \rightarrow \frac {1}{l^2}$
D
$\Delta l \rightarrow l$
(AIPMT-2014)
Solution
As $V=Al$ $…..(i)$
where $A$ is the area of $cross-section$ of the wire.
$Young's\,modulus,\,Y = \frac{{\left( {F/A} \right)}}{{\left( {\Delta l/l} \right)}} = \frac{{Fl}}{{A\Delta l}}$
$\Delta l = \frac{{Fl}}{{YA}} = \frac{{F{l^2}}}{{YV}}$ $(Using(i))$
$\Delta l \propto {l^2}$
Hence, the graph between $\Delta l$ and ${l^2}$ is a straight line.
Standard 11
Physics
