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. 16 J
B. 8 J
C. 4 J
D. `(1)/(4)J`

Answer

A

Explanation

`w=(1)/(2)F Delta l=(1)/(2) (AY)/(L)(Delta l)^(2)`
`(w^(2))/(w_(1))=((R_(2))/(R_(1)))^(2) xx ((L_(1))/(L_(2)))`
`(w_(2))/(2)=4xx2=8`
`w_(2)=16J`