Two forces F _1 and F _2 are acting on a body. One force has...

Two forces

\bar{F}_1

and

\bar{F}_2

are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between

\vec{F}_1

and

\vec{F}_2

\cos ^{-1}\left(\frac{1}{n}\right)

. The value of

|n|

is _____.

Correct answer

Step-by-step solution

\begin{aligned} & \left|\vec{F}_1\right|=\mathrm{F} \\ & \left|\overrightarrow{\mathrm{F}}_{\mathrm{R}}\right|=\left|\overrightarrow{\mathrm{F}_2\right|=3 \mathrm{~F} \\ & \mathrm{~F}_{\mathrm{R}}^2=\mathrm{F}_1^2+\mathrm{F}_2^2+2 \mathrm{~F}_1 \mathrm{~F}_2 \cos \theta \\ & 9 \mathrm{~F}^2=\mathrm{F}^2+9 \mathrm{~F}^2+6 \mathrm{~F}^2 \cos \theta \\ & \cos \theta=-\frac{1}{6} \\ & \theta=\cos ^{-1}\left(\frac{1}{-6}\right) \\ & \mathrm{n}=-6 \\ & |\mathrm{n}|=6\end{aligned}

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