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

Answer

d

Explanation

As, `W = (1)/(2) F Delta l` (where, `Delta l` = entension)
`implies W = (1)/(2) xx (Y pi r^(2) Delta I)/(I) Delta I` or `W = (Y pi r^(2) Delta I)/(2I)`
Where, `Y = (FI)/(pi r^(2) Delta I)` and `F = (Y pi r^(2) Delta I)/(I)`
`implies W prop (r^(2))/(I)` and `W prop ((2r)^(2)2)/(I)`
`implies (W')/(W) = 8` or `W = 8 xx 2 J = 16 J`