Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

Copper of fixed volume $V$ is drawn into a 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?

$\Delta l$ vs $1/l$

$\Delta l$ vs $l^2$

$\Delta l$ vs $1/l^2$

$\Delta l$ vs $l$

Step-by-Step Solution

Young's Modulus Formula: Young's modulus ( $Y$ ) is defined as the ratio of longitudinal stress to longitudinal strain: $Y = \frac{F/A}{\Delta l/l}$ .
Rearranging for Extension: $\Delta l = \frac{Fl}{AY}$ .
Volume Constraint: Since the volume ( $V$ ) of the wire is fixed and $V = A \times l$ , we can substitute the area $A$ with $V/l$ .
Substitution: $\Delta l = \frac{Fl}{(V/l)Y} = \frac{F l^2}{VY}$
Analysis: Since $F$ , $V$ , and $Y$ are constants for the given copper wire, $\Delta l$ is directly proportional to the square of the length ($
$\Delta l \propto l^2$
Graphical Representation: To obtain a straight line graph ( $y = mx$ ), we must plot $\Delta l$ on the y-axis and $l^2$ on the x-axis. Therefore, the graph of $\Delta l$ versus $l^2$ is a straight line.

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