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

Answer

A

Explanation

Stretching force `F=(Ypir^2triangleL)/(L)`
where the symbols have their unual meanings. Both the wires are of same material, so Y will be equal, extension in both the wires is same so `triangleL` will be equal .
`therefore Fprop(r^(2))/(L)`
`therefore(F')/(F)=((2r)^(2))/((L//2))xx(L)/(r^(2))=8`
or `F'=8F` .`(i)`
Work done in stretching a wire,
`W=(1)/(2)xxFxxDeltaL`
For same extension `WpropF`
`(W`)/(W)=(F`)/(F)=8` [Using (i)]
`W'=8Wxx2J=16J`