Copper of fixed volume V is drawn into wire o | vedclass

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Question

As $V=Al$                                        &

Vedclass · Accepted Answer

$\Delta l \rightarrow  l^2$

Vedclass · Answer

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.

Column $-I$	Column $-II$
$(a)$ image	$(i)$ $A$ is ductile
$(b)$ image	$(ii)$ $A$ is brittle
	$(iii)$ $B$ is ductile
	$(iv)$ $B$ is brittle

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?

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