Question 41 of 118

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of wire is $62.8cm$ and its diameter is $4mm$. The Young's modulus is found to be $x\times {10}^{4}N{m}^{-2}$
The value of $x$ is _______.

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Answer: 5

Given here, $L=62.8cm\text{and}d=4mm$.

From the given graph, we can see that extension in wire is linearly dependent on force applied. Slope of the curve is $\tan 45^{\circ}=1$.
So, $F=\Delta L$
Young's modulus is given by $Y=\dfrac{FL}{A\Delta L}$, where, $A$ is area of wire.
$\Rightarrow Y=\dfrac{L}{A}$
$\Rightarrow Y=\dfrac{62.8\times {10}^{-2}}{\pi {\left(2\times {10}^{-3}\right)}^{2}}$
$\Rightarrow Y=5\times {10}^{4}N{m}^{-2}$