A particle moves from a point `(- 2 hati + 5 hatj) ` to `(4 hatj + 3hatk)` when a force of `(4 hati + 3hatj) N` is applied. How much work has been done by the force?

Options

A. 8J
B. 11 J
C. 5 J
D. 2 J

Answer

C

Explanation

Here, `vec(r_1) = (-2hati + 5hatj) m, vec(r_2) = (4 hatj + 3 hatk)m`
`vecF = (4 hati + 3 hatj) N, W = ?`
Work done by force F in moving from `vec(r_1) ` to `vec(r_2)`
`W = vecF . (vec(r_2) - vec(r_1)) = (4hati + 3hatj) . (4 hatj + 3hatk + 2 hati - 5 hatj)`
`= (4 hati + 3 hatj) . (2 hati - hatj + 3 hatk) = 8 + (-3) = 5 J`.