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

Options

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

Answer

D

Explanation

Stress = Y strain
` (mg)/(pi r^(2))=(y Delta l_(1))/(l) `
` implies Delta l_(1) = (mg l)/(pi y r^(2))`
if ` r' =(r )/(2) `
`implies Delta l_(2) =(mgl)/(pi y ((l)/(2))^(2))=4Delta l_(1)`
` Delta l_(2) = 4xx2.00 = 8.00mm`