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. `3/2J`
D. `7/5 J`

Answer

`(2)`

Explanation

`W = int_(0,0)^(1,1)vecF. vec ds.`
here `vec ds = dx hat i + dy hat j + dz hat k`
`therefore W = int_((0,0)^(1,1))(x^(2)dy + y dx) = int_((0,0)^(1,1)) (y^(2)dy + x.dx)`
`(as x = y)`