A uniform force of `(3 hati + hatj)` newton acts on a particle of mass 2 kg. Hence the particle is displaced from position `(2hati + hatk)` meter to position `(4 hati + 3hatj - hatk)` meter. The work done by the force on the particle is

Options

A. 13 J
B. 15 J
C. 9 J
D. 6 J

Answer

C

Explanation

Here, `vecF = (3 hati + hatj)N, vec(r_1) = (2hati + hatk) m`,
`vec(r_2) = (4hati + 3hatj - hatk) m`
Displacement , `vecr = vec(r_2) - vec(r_1)`
`vecr = (4 hati + 3 hatj - hatk) m - (2 hati + hatk) m = 2 hati + 3hatj - 2hatk m`
Work done ,
`W = vecF.vecr = (3hati + hatj) . (2hati+ 3 hatj - 2hatk) = 6 + 3= 9 J = 6 + 3 = 9 J` .