Question

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

Answer 1

Correct Answer - B
`W = underset(((0,0))) overset(((1,1)))int vec F. vecds`, Here `vec ds = dx hat i + dy hat j + dz hat k`
`:. W = underset(((0,0))) overset(((1,1)))int (x^(2) dy + ydx) = underset(((0,0))) overset(((1,1)))int (y^(2) dy + x.dx)`
(as `x = y`).