Question

$100$ coplanar forces each equal to $10 N$ act on a body. Each force makes an angle $\dfrac{\pi}{50}$ with the preceding force. What is the resultant of the forces?
a) $1000 N$
b) $500 N$
c) $250 N$
d) Zero

Answer 1

Coplanar forces are forces on a single face. It means that all application points are inside that face and that all forces are going parallel to that plane. When all forces are operating in the same plane, they are named coplanar, whereas when forces are exerted at the same time at the same point, they are described as concurrent forces. In this question, we will find the total angle made which is the product of the number of forces and the angle made by each force.

Complete step-by-step solution:
$100$ coplanar forces each equal to $10 N$ act on a body.
Each force makes an angle $\dfrac{\pi}{50}$ with the preceding force.
All $100$ forces will cover the angle.
Total Angle = $100 \times \dfrac{\pi}{50}$
$\implies \textit{total angle} = 2 \pi$
Therefore, each force acts opposite to each other.
These vectors form a closed polygon.
All the forces through one point will pass and all the forces will be balanced.
Therefore, the Resultant Force will be Zero.
Option (d) is correct.

Note: Coplanar forces may be concurrent, parallel, non-concurrent, or non-parallel. A concurrent force comprises at least two forces where all lines of action come collectively at a general point. A non-parallel and non-concurrent force has vectors that are not parallel and not meeting at a single point. These are the most complex forces to resolve because they are a mixture of forces. A parallel force holds at least two forces where all action lines are parallel.