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

Options

A. (A) `8 J`
B. (B) `16 J`
C. (C) `4 J`
D. (D) `32 J`

Answer

B

Explanation

`W = U = 1/2F(Deltal) = (1)/(2).(YA(Deltal)^(2))/l`
`:. U prop A/l` (`:.` In both the cases Deltal is same )
`U_(2)/U_(1) = A_(2)/A_(1) .l_(1)/l_(2) = (r_(2)/r_(1))^2.l_1/l_2 =(4)(2)`
`:. U_(2) = 8U_(1) = 8(2) = 16J`