Question

The sum of n vectors each of magnitude F
lying in a plane and acting
simultaneously on a body at angle 2pi/n
with preceding is given by:
a) F
b) 2piF
c) nF
d) zero​

Answer 1

Answer:

Correct option is D (Zero)

Explanation:

Given that:

Total forces=N

An angle between forces=N2π

Therefore,

Total angle between N co-planer force =N2π×N=2π

Thus, the forces represent a polygon of N sides.

As, by the polygon method of vector addition, the vectors can be added by the placing the vectors in order as the sides of the polygon and the resultant of these vectors will join them to the tail of the first vector to head of the last vector. This will close the polygon and will give the magnitude and the direction of the resultant vector.

As the N number forces mentioned above, represents a closed polygon, the resultant will be zero.