The force constant of a wire is K and that of another wire of the same material is 2K. When both the wires are stretched by the same force, then the relation between the works done in the two cases is

Options

A. `W_(2) = W_(1)`
B. `W_(2) = 0.5 W_(1)`
C. `W_(2) = 2W_(1)`
D. `W_(2) = 2W_(1)^(2)`

Answer

B

Explanation

`x_(1) = (F)/(K) , x_(2) = (F)/(2K) :. x_(2) = (x_(1))/(2)`
`because W_(1) = Fx_(1) and W_(2) = Fx_(2) :. W_(2) = 0.5 W_(1)`