A uniform force of (3i + j) newton acfs on a particle of mass 2kg. The particle is displaced from position (2i + k) meter to position (4i + 3j – k) meter. The work done by the force on the particle is

Options

(a) 6 J
(b) 13 J
(c) 15 J
(d) 9 J

Correct Answer:

9 J

Explanation:

Given : F⃗ = 3i + j
r⃗₁ = (2i + k), r⃗₂ = (4i + 3j – k⃗)
r⃗ = r⃗₂ – r⃗₁ = (4i + 3j – k⃗) – (2i + k)
or r⃗ = 2i + 3j – 2k
so, work done by the given force w = f⃗ . r⃗
= (3i + j) x (2i + 3j – 2k) = 6 + 3 = 9 J