Question

The extension of a wire by the application of a load is $0.3cm$. The extension in the wire of the same material but of double the length and half the radius of cross section in cm is

• A. $3$
• B. $0.3$
• C. $1.2$
• D. $2.4$

Answer 1

The correct option is D $2.4$

$\Delta l=\frac{Fl}{Y\pi r^2}$
$\frac{\Delta l_1}{\Delta l_2}=\frac{Fl}{Y\pi r^2}\times \frac{Y\pi {\left(\frac{r}{2}\right)}^2}{F2l}$
$\frac{\Delta l_1}{\Delta l_2}=\frac{1}{8}$
$8\Delta l_1=\Delta l_2$
So, $\Delta l_2=8\left(0.3\right)$
$=2.4cm$