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

Options

A. 16
B. 8
C. 4
D. frac{1}frac{4}

Answer

A

Explanation

Force, `F=(ypir^(2)Deltal)/l`
`F propto r^(2)/l` [`because` Material is same and tE is equal]
`F_(1)/F_(2) = r_(1)^(2)/r_(2)^(2) xx l_(2)/l_(1) = r_(1)^(2)/((2n)^(2))xxl_(1)/(2l_(1)) = 1/8`
`therefore F_(2) = 8F_(1)`
Ratio of work done,
`W_(1)/W_(2) = (F_(1)Deltal)/(F_(2)Deltal) = F_(1)/F_(2)`
`2/W_(2) = 1/8`
`therefore W_(2) = 16J`