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 `R/2` and other conditions remaining the same, the increase in its length is

Options

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

Answer

D

Explanation

Change in length, `Delta l =(mgl)/(pir^(2)E)`
`(Deltal_(1))/(Delta l_(2)) = [r_(2)/r_(1)]^(2) [ because Deltal propto 1/r^(2)`
`therefore Delta l_(2) = 8mm`