Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 40√3, the magnitude of each force is

Question

Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 40√3, the magnitude of each force is (A) 40 N (B) 20 N (C) 80 N (D) 30 N

Tardigrade Admin · Accepted Answer

Let equal forces F1 = F2 = F Newton. Angle between the forces (θ ) = 60° Resultant force R = √F21 + F22 + 2F1F2 cos θ ∴ 40√3 = √F2 + F2 + 2F ⋅ F cos 60° or F = 40 N

Q. Two equal forces are acting at a point with an angle of 60 $^{\circ}$ between them. If the resultant force is equal to $403$ , the magnitude of each force is

40 N

20 N

80 N

30 N

10 N

Let equal forces $F_{1} = F_{2} = F$ Newton.
Angle between the forces $(θ) = 6 0^{\circ}$
Resultant force $R = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} cos θ$
$∴ 403 = F^{2} + F^{2} + 2 F \cdot F cos 6 0^{\circ}$
$or F = 40 N$

Q. Two equal forces are acting at a point with an angle of 60∘ between them. If the resultant force is equal to 403​, the magnitude of each force is