Question

Five equal force of $10$N each applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be

• A. zero
• B. $10$N
• C. $20$N
• D. $10\sqrt{2}$

Answer 1

The correct option is A zero

It is clear that all the vectors are inclined at equal plane w.r.t each other. Also since all the forces lie in the same plane the resultant will be a zero vector would cancel each other. Even in real life if we pull an object with the same force from different positions with equal angles between each force the object would not move.

If mathematically calculated then,

Angle between the forces $Q=\frac{360}{5}={72}^0$

Resultant can be calculated $F_R=\frac{F\sin \frac{N\theta }{2}}{\sin \frac{\theta }{2}}$

On Substituting we get $F_R=0$.