Question

Three forces each of magnitude $F$ are applied along the edges of a regular hexagon as shown in the figure. Each side of hexagon is $a$. What is the resultant moment (torque) of these
three forces about centre $O?$

• A. $3aF$
• B. $\frac{\sqrt{3}}{2}aF$
• C. $\frac{3\sqrt{3}}{2}aF$
• D. $\frac{1}{2}aF$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}aF$

From the figure.

The resultant moment about the center O is
$\tau =\left(\frac{\sqrt{3}}{2}a\right)F-\left(\frac{\sqrt{3}}{2}a\right)F+\left(\frac{\sqrt{3}}{2}a\right)F$
$\tau =\left(\frac{\sqrt{3}}{2}a\right)F$