Mechanical Properties of Solids - Result Question 4
5. 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 wi re is ’ $\Delta l$ ‘. Which of the following graphs is a straight line?
[2014]
(a) $\Delta l$ versus $\frac{1}{l}$
(b) $\Delta l$ versus $l^{2}$
(c) $\Delta l$ versus $\frac{1}{l^{2}}$
(d) $\Delta l$ versus $l$
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Solution:
- (b) As $Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}} \Rightarrow \Delta l=\frac{F l}{AY}$
But $V=A l$ so $A=\frac{V}{l}$
Therefore $\Delta l=\frac{F l^{2}}{VY} \propto l^{2}$
Hence graph of $\Delta l$ versus $l^{2}$ will give a straight line.
