Question

Five equal forces of $10N$ each are 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. $10N$
• C. $20N$
• D. $10\sqrt{2}N$

Answer 1

The correct option is A

Zero

Explanation for the correct option:

Step 1: Find the angle between forces.

We have been the five equal forces of $10N$each are applied at one point and all are lying in one plane.

We need to find the resultant force if the angles between them are equal.

Let $F_1,F_2,F_3,F_4,F_5$ be five forces of $10N$ each and all are lying in one plane.

Also, angles between them are equal.

So, the angle between any two forces would be,

$\Rightarrow \frac{360°}{5}=72°$

Step 2: Find the resultant force.

Since the magnitude of each force vector is equal and they all are equally lying in one plane.

So, the resultant force vector would be,

$\Rightarrow F_r=F_i\frac{\sin {\displaystyle \frac{N\theta }{2}}}{\sin {\displaystyle \frac{\theta }{2}}}$

where, $F_i$ be any force and $F_i=10$

$\theta =72°,N=5$

$$\begin{gathered} \Rightarrow F_r=10\times \frac{\sin {\displaystyle \frac{5\times 72}{2}}}{\sin {\displaystyle \frac{72}{2}}} \\ \Rightarrow F_r=10\times \frac{\sin {\displaystyle \frac{360}{2}}}{\sin {\displaystyle \frac{72}{2}}} \\ \Rightarrow F_r=10\times \frac{\sin 180°}{\sin 36°} \\ \Rightarrow F_r=10\times 0 \\ \Rightarrow {\mathit{F}}_{\mathbf{r}}\mathbf{=}\mathbf{0} \end{gathered}$$

Therefore, option (A) is the correct answer.