A wire of length L and radius r is rigidly fi | vedclass

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(D) Young's modulus $Y$ is given by the formula: $Y = \frac{F L}{A l} = \frac{F L}{\pi r^2 l}$.For the first wire: $Y = \frac{F L}{\pi r^2 l} \quad \d

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$l$

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(D) Young's modulus $Y$ is given by the formula: $Y = \frac{F L}{A l} = \frac{F L}{\pi r^2 l}$.For the first wire: $Y = \frac{F L}{\pi r^2 l} \quad \dots (i)$.For the second wire,the parameters are: $L' = 2L$,$r' = 2r$,$F' = 2F$,and let the new elongation be $l'$.Since the material is the same,the Young's modulus $Y$ remains constant.$Y = \frac{F' L'}{\pi (r')^2 l'} = \frac{(2F) (2L)}{\pi (2r)^2 l'} = \frac{4 F L}{\pi (4 r^2) l'} = \frac{F L}{\pi r^2 l'} \quad \dots (ii)$.Comparing equations $(i)$ and $(ii)$:$\frac{F L}{\pi r^2 l} = \frac{F L}{\pi r^2 l'}$.Therefore,$l' = l$.

$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in length is $l$. If another wire of the same material but double the length and double the radius is stretched with a force $2F$,then the increase in length is:

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