Question

The square of the resultant of two equal forces acting at a point is equal to three times their product. Angle between them is

• A. $30^{\circ }$
• B. $45^{\circ }$
• C. $60^{\circ }$
• D. $90^{\circ }$

Answer 1

Answer: (C)

Let two forces be $F_1$ and $F_2$ acting at a point and angle between them is $\theta$.
Resultant of $F_1$ and $F_2$ is given by
$F=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$ ....(i)
According to question,
$F^2=3F_1{F}_2=3F_{1^2}[\because F_1=F_2]$
$F^2=F_{1^2}+F_{2^2}+2F_1{F}_2\cos \theta$
or $3F_{1^2}+F_{1^2}+2F_{1^2}\cos \theta$
or, $3=1+1+2\cos \theta$
or, $\cos \theta =\frac{1}{2}$
or, $\theta ={\cos }^{-1}\left(\frac{1}{2}\right)=60^{\circ }$