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Physics-

General

Easy

Question

A wire of length $2 L$ and radius $r$ is stretched between $A$ and $B$ without the application of any tension. If $Y$ is the Young’s modulus of the wire and it is stretched like $A C B$ , then the tension in the wire will be

$\frac{π r^{2} Y d^{3}}{2 L^{2}}$
$\frac{π r^{2} Y d^{2}}{2 L^{2}}$
$\frac{π r^{2} Y . 2 L^{2}}{d^{2}}$
$\frac{π r^{2} Y . 2 L}{d}$

The correct answer is: $fraction numerator pi r to the power of 2 end exponent Y d to the power of 2 end exponent over denominator 2 L to the power of 2 end exponent end fraction$

$T equals fraction numerator Y A l over denominator L end fraction$
Increase in length of one segment of wire
$l equals open parentheses L plus fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction close parentheses minus L equals fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction$
So, $T equals fraction numerator Y pi r to the power of 2 end exponent. d to the power of 2 end exponent over denominator 2 L to the power of 2 end exponent end fraction$

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