Question

Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a. At point B, the wqivalent force and couple are, respectiely.

• A. F ($\leftarrow$) and $3\sqrt{3}Fa$ (clockwise)
• B. F ($\to$) and zero
• C. F ($\leftarrow$) and $\sqrt{3}Fa$ (counter clockwise)
• D. F ($\to$) and $3\sqrt{3}Fa$ (counter clockwise)

Answer 1

The correct option is D F ($\to$) and $3\sqrt{3}Fa$ (counter clockwise)

By polygon law resultant is closing side of polygon taken in reverse order.



Take moment about point B

$M_B=F\times a\times cos30+F\times a\times sin60\times 2+F\times 2a\times sin60+F\times a\times cos30=3\sqrt{3}Fa$

$\therefore$ $M_B=3\sqrt{3}Fa$