Question

The vector sum of (N) coplanar forces, each of magnitude F, when each force is making an angle of
$\frac{2\pi }{N}$ with that preceding one, is :

• A. F
• B. $\frac{NF}{2}$
• C. NF
• D. Zero

Answer 1

The correct option is D Zero

Given that:

Total forces$=N$

An angle between forces$=\frac{2\pi }{N}$

Therefore,

Total angle between $N$ co-planer force $=\frac{2\pi }{N}\times N=2\pi$

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.