A body is displaced from `(0,0)` to `(1 m, 1m)` along the path `x = y` by a force `F=(x^(2) hatj + y hati)N`. The work done by this force will be

Options

A. `(4)/(3) J`
B. `(5)/(6) J`
C. `(3)/(2) J`
D. `(7)/(5) J`

Answer

B

Explanation

`W = int_(((0,0)))^(((1,1))) vec F.vec ds`
Here `=vec(dx) =dx hati + dy hatj+dx hatk`
`W =int_(((0,0)))^(((1,1)))(x^(2)dy+ydx)(as x=y)`
`W=[(y^(3))/(3)+(x^(2))/(2)]_((0,0))^((1,1)) =(5)/(6)J`.