Three ants 1, 2 and 3 are pulling a grain with forces of magnitudes `2Nsqrt(3)N` and `sqrt(2)N` and as shown in the figure. Find the resultant force acting on the grain.

Options

A. zero N
B. `(l hati)` N
C. `(-1 hat i)` N
D. `(l hat j)` N

Answer

b

Explanation

The forces exerted by the ants are given as `F_(1)=2(cos 30^(@)+sin 30^(@)hatj)=sqrt(3hat i+j`
the net force is `overset(rarr)F=overset(rarr)F_(1)+overset(rarr)F_(2)+overset(rarr)F_(3)`
we have `overset(rarr)F=sqrt(3hati+hatj)+-sqrt(3hati)+(hati-hatj)=1hatN`