Answer :

According to the given figure, the young’s modulus is given by the expression :

Y = (f/A)(L/l)

First case: Let the length of the wire be L and the radius of wire be r. Force applied = f and the Increase in length is represented by l.

${{Y}_{1}}=\frac{\frac{f}{\pi {{r}^{2}}}}{\frac{l}{L}}=\frac{fL}{\pi {{r}^{2}}l}$

Second case: Let the length of the wire be 2L and the radius of wire be 2r. Force applied = 2f and the Increase in length is represented by 2l.

${{Y}_{2}}=\frac{\frac{f}{\pi 2{{r}^{2}}}}{\frac{x}{2L}}=\frac{fL}{\pi {{r}^{2}}x}$

Therefore, it can be concluded that x = l.