If the work done in stretching a wire by 1 mm is 2J, then work necessary for stretching another wire of same material but with double radius of corss-section and half the length by 1 mm is

Options

A. 4
B. 8
C. 2
D. 16

Answer

D

Explanation

`w_(1)=(1)/(2) F_(1)l_(1) and w_(2) =(1)/(2)F_(2)l_(2)`
`(w_(2))/(w_(1))=(F_(2))/(F_(1)) xx ((A_(2))/(A_(1)))^(2)xx(L_(1))/(L_(2))`