Question

$50$ coplanar forces each equal to $100 N$ act on a body. Each force makes angle $1/25$ with the preceding force. What is the resultant of the forces?
A. $5000 N$
B. $0.5 N$
C. Zero
D. $41 N$

Answer 1

Hint: Calculate the total angle covered by the forces acting on the body. If this angle is equal to \[2\pi \], then we can say that the forces are acting on the body from all directions. Each force on the body will be opposite to the force that is acting on the other side of the body.

Complete step by step answer:
We have given that total 50 forces are acting on the body and each force is making an angle 1/25 with the preceding force.

Let’s calculate the total angle covered by the forces on the body as follows,
One force covers an angle \[\dfrac{\pi }{{25}}\] then 50 forces will cover an angle equal to,
\[\theta = \left( {50} \right)\left( {\dfrac{\pi }{{25}}} \right)\]
\[ \Rightarrow \theta = 2\pi \]

Therefore, we can see the total forces will cover the whole circle of the body. Thus, all the forces acting on the body will pass through the centre of the body and each force will be opposite to the force acting on the other side of the body. Thus, in this situation each force will be balanced by the other force and the total force on the body will be sum up to zero.

So, the correct answer is option C.

Note:Whether the force is large or small, if the two forces of the same magnitude act on the opposite sides of the body, the resultant force on the body becomes zero. If we apply a force on the body in the positive x-direction and there is friction acting on the body which is always opposite to the applied force. If the frictional force is equal to the applied force, the net force on the body will be zero and the body will not move.