Question

A body is displaced from (0, 0) to (1 m, 1 m) along the path x = y by a force F = (x²`hat"J"` + y`hat"i"`)N. The work done by this force will be:

Options

• `4/3`J

• `5/6`J

• `3/2`J

• `7/5`J

Answer 1

`bb(5/6)`J

Explanation:

W = `int_((0","0))^((1","1)) vec"F".vec"d"x`

Here d`vec"s" = "d"xhat"i" + "dy"hat"j" + "dz"hat"k"` 

∴ W = `int_((0","0))^((1","1))`(x²dy + ydx)

= `int_((0","0))^((1","1))`(x²dy + x.dx) (as x = y)

∴ W = `["y"^3/3+x^2/2]_((0","0))^((1","1))`

= `5/6` J