If the work done in strectching 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. `1/4J`
B. `4J`
C. `8J`
D. `16J`

Answer

B

Explanation

`W=1/2F/_\l`
`W=1/2xx(Ypir^(2)/_\l)/l/_\l `and `Y=(Fl)/(pir^(2)/_\l)`
or `W=(Ypir^(2)/_\l^(2))/(2l)` and `F=(Ypir^(2)/_\l)/l`
or `Wprop(r^(2))/l, W'prop((2r)^(2)2)/l`
`W'=W=8` or `W'=8xx2J=16J`