Two forces of equal magnitude F act at a point. If the angle between them is θ, then the magnitude of the resultant force is

Question

Two forces of equal magnitude F act at a point. If the angle between them is θ, then the magnitude of the resultant force is (A) F√2(1-sin θ ) (B) F√2(1+sin θ ) (C) 2 F sin (θ/2) (D) 2 F cos ((θ /2))

Tardigrade Admin · Accepted Answer

Here, F1 = F2 = F The magnitude of the resultant force is FR=√F21+F22+2F1F2 cos θ=√F2+F2+2(F)(F)cos θ =√2F2+2F2 cos θ =F√2(1+cos θ ) =F√2(2 cos2 (θ/2))=2F cos((θ/2))

Q. Two forces of equal magnitude $F$ act at a point. If the angle between them is $θ$ , then the magnitude of the resultant force is

$F 2 (1 - s in θ)$

$F 2 (1 + s in θ)$

$2 F s in \frac{θ}{2}$

$2 F cos (\frac{θ}{2})$

Here, $F_{1} = F_{2} = F$
The magnitude of the resultant force is
$F_{R} = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} cos θ = F^{2} + F^{2} + 2 (F) (F) cos θ$
$= 2 F^{2} + 2 F^{2} cos θ = F 2 (1 + cos θ)$
$= F 2 (2 co s^{2} \frac{θ}{2}) = 2 F cos (\frac{θ}{2})$

Q. Two forces of equal magnitude F act at a point. If the angle between them is θ, then the magnitude of the resultant force is

F2(1−sinθ)​

F2(1+sinθ)​

2Fsin2θ​

2Fcos(2θ​)