A force is applied to a steel wire A , rigidly clamped at one end....

As we know, $Y = \dfrac{F}{\dfrac{A}{\dfrac{∆ l}{l}}}$

$⇒ F = \dfrac{YA}{l} ∆ l$

For both cases force applied is the same, therefore

${\left(\dfrac{YA ∆ l}{l}\right)}_{1} = {\left(\dfrac{YA ∆ l}{l}\right)}_{2}$

$⇒ \dfrac{∆ {l}_{2}}{∆ {l}_{1}} = \dfrac{{A}_{1}}{{A}_{2}} \times \dfrac{{l}_{2}}{{l}_{1}}$

$⇒ \dfrac{∆ {l}_{2}}{0 . 2} = \dfrac{\pi{R}^{2}}{\pi{\left(2 . 4R\right)}^{2}} \times \dfrac{2}{1}$

$⇒ ∆ {l}_{2} = 6 . 9 \times {10}^{- 2}mm$