Question

Two equal forces are acting at a point with an angle of 60$^{\circ}$ between them. If the resultant force is equal to $40\sqrt{3}$, the magnitude of each force is

• A. 40 N
• B. 20 N
• C. 80 N
• D. 30 N

Answer 1

Answer: (A)

40 N

Answer 2

The correct option is(A): 40 N.

Let equal forces $F_1 = F_2 = F$ Newton.
Angle between the forces $(\theta ) = 60^\circ$
Resultant force $\ \ R = \sqrt{F^2_1 + F^2_2 + 2F_1F_2 \\\cos \ \theta}$
$\therefore \ \ \ \ \ \ \ \ \ 40\sqrt{3} = \sqrt{F^2 + F^2 + 2F \cdot F \ \cos \ 60^\circ}$
$or \ \ \ \ \ \ \ \ \ \ \ F = 40 \ N$