Two constant forces `vecF_1` and `vecF_2` act on a body of mass `8kg`. These forces displace the body from point `P(1, -2, 3)` to `Q` `(2, 3, 7)` in `2s` starting from rest. Force `vecF_1` is of magnitude `9N` and is acting along vector `(2hati-2hatj+hatk)`. Work done by the force `vecF_2` is

Options

A. (a) `80J`
B. (b) `-80J`
C. (c) `-180J`
D. (d) `180J`

Answer

D

Explanation

`vecs=hati+5hatj+4hatk=1/2((vecF_1+vecF_2)/(m))(2)^2` (i)
`vecF_1=(9(2i-2j+k))/(sqrt(2^2+2^2+1))=6i-6j+3k` (ii)
From Eqs. (i) and (ii), `vecF_2=-2hati+26hatj+13hatk`
Work done by `vecF_2: W=vecF_2.vecs=180J`