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 $\vec{F}_2$ is $\cos ^{-1}\left(\frac{1}{n}\right)$. The value of…

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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 $\vec{F}_2$ is $\cos ^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is _____.

Aicharya · Accepted Answer

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

Two forces $\bar{F}_1$ and $\bar{F}_2$ are acting on a body. One force has magnitude thrice that of the…

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