Question

When a uniform wire of radius r is stretched by a $2kg$ weight, the increase in its length is $2.00mm$. If the radius of the wire is $r/2$ and other conditions remain in the same, increase in its length is

• A. $2.00mm$
• B. $4.00mm$
• C. $6.00mm$
• D. $8.00mm$

Answer 1

The correct option is D $8.00mm$

$Y=\frac{F/A}{△l/l}$ (standard result)

$△l=\frac{Fl}{\pi r^{2}Y}$

$\frac{2}{1000}=\frac{Fl}{\pi (\frac{r}{2}{)}^{2}Y}$

$△l_1=\frac{Fl}{\pi (\frac{r}{2}{)}^{2}Y}$

$=\frac{Fl}{\pi r^{2}Y}$

$=4\left(\frac{2}{1000}\right)$

$=\frac{8}{1000}m$

$=8mm$