Question

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

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

Answer 1

The correct option is B $\text{Zero}$

Let the forces are
$\overrightarrow{F_1},\overrightarrow{F_2},\overrightarrow{F_3},\overrightarrow{F_4},\overrightarrow{F_5}$
Now, we must find the resultant,
$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}+\overrightarrow{F_4}+\overrightarrow{F_5}$
Since forces acting at the point have same angel between them and also acting in the plane, therefore joining the rail of one with the head of other will form a regular pentagon.
By polygon rule of vector addition,
$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}+\overrightarrow{F_4}+\overrightarrow{F_5}=0$
So, the resultant force will be $0$
Final Answer:(A)