When a uniform wire of radius $r$, is stretched by a $2\;kg$ weight the increase in its length is $2.00\; mm$ If the radius of the wire is $\frac{r}{2}$ and other conditions remining the same, the increase in its length is :

Question

( A ) 4.00 mm
( B ) 6.00 mm
( C ) 2.00 mm
( D ) 8.00 mm