Resultant of two equal vectors acting at right angle to each other is 14.14 unit. The magnitude of each force is

Question

Resultant of two equal vectors acting at right angle to each other is 14.14 unit. The magnitude of each force is (A) 5 unit (B) 10 unit (C) 20 unit (D) 30 unit

Tardigrade Admin · Accepted Answer

Let F1 = F2 = x Here, resultant, R = 14.14 unit and θ = 90° R2 = F2 + F2 = 2F2 i.e. R = √2x2 i.e. 14.14 = √2x2 or x = (14.14/√2) = (14.14/1.414) = 10 unit since F1 = F2 = 10 unit.

Q. Resultant of two equal vectors acting at right angle to each other is 14.14 unit. The magnitude of each force is

5 unit

10 unit

20 unit

30 unit

Let $F_{1} = F_{2} = x$ Here, resultant, R = 14.14 unit and $θ$ = 90 $^{\circ}$ $R^{2} = F^{2} + F^{2} = 2 F^{2}$ i.e. R = $2 x^{2}$ i.e. 14.14 = $2 x^{2}$ or $x = \frac{14.14}{2} = \frac{14.14}{1.414}$ = 10 unit since $F_{1} = F_{2} =$ 10 unit.

Q. Resultant of two equal vectors acting at right angle to each other is 14.14 unit. The magnitude of each force is

5 unit

10 unit

20 unit

30 unit

Let F1​=F2​=x Here, resultant, R = 14.14 unit and θ = 90∘ R2=F2+F2=2F2 i.e. R =2x2​ i.e. 14.14 = 2x2​ or x=2​14.14​=1.41414.14​ = 10 unit since F1​=F2​= 10 unit.

Let $F_{1} = F_{2} = x$ Here, resultant, R = 14.14 unit and $θ$ = 90 $^{\circ}$ $R^{2} = F^{2} + F^{2} = 2 F^{2}$ i.e. R = $2 x^{2}$ i.e. 14.14 = $2 x^{2}$ or $x = \frac{14.14}{2} = \frac{14.14}{1.414}$ = 10 unit since $F_{1} = F_{2} =$ 10 unit.