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

Tardigrade Admin · Accepted Answer

Given: Force F1= force F2=F or F1=F2=F Resultant force R=40 √3 N Angle between two forces F1 and F2 is θ=60° ∴ R=√F12+F22+2 F1 F2 cos θ or 40 √3=√F2+F2+2 F2 cos 60°=√3 F2 or F=40 N

Q. Two equal forces are acting at a point with an angle of $6 0^{\circ}$ between them. If the resultant force is equal to $403 N$ , the magnitude of each force is

40 N

20 N

80 N

30 N

Given : Force $F_{1} =$ force $F_{2} = F$
or $F_{1} = F_{2} = F$
Resultant force $R = 403 N$
Angle between two forces $F_{1}$ and $F_{2}$ is $θ = 6 0^{\circ}$
$∴ R = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} cos θ$
or $403 = F^{2} + F^{2} + 2 F^{2} cos 6 0^{\circ} = 3 F^{2}$
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​N, the magnitude of each force is