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

Answer

B

Explanation

Work done `W=(1)/(2)kx^(2)`
`(W_(2))/(W_(1))=(k_(2))/(k_(1))`
But `k=(yA)/(l)` or `(k_(2))/(k_(1))=(A_(2))/(A_(1))(l_(1))/(l_(2))`
Here, Y is same for both wires
`therefore(W_(2))/(W_(1))=(A_(2))/(A_(1))xx(l_(1))/(l_(2))`
Here, Y is same for both wires
`therefore(W_(2))/(W_(1))=(A_(2))/(A_(1))xx(l_(1))/(l_(2))`
`(W)/(2)=((r_(2))/(r_(1)))^(2)(l_(1))/(l_(2))=(2)^(2)xx1`
`impliesW=8J`