Two forces, \(\mathbf{F}_{1}\) and \(\mathrm{F}_2\) are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is
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Let smaller force = F
Then greater force = 2F
Resultant is equal to greater force:
R = 2F
Using formula:
\(R^{2} = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} \cos \theta\)
\((2F)^2 = F^2 + F^2 + 2(F)(2F) \cos \theta\)
\(4F^{2} = F^{2} + 4F^{2} + 4F^{2} \cos \theta\)
\(-1 = 4 \cos \theta\)
\(\cos \theta = - \frac{1}{4}\)
\(\theta = \cos^{-1} \left( -\frac{1}{4} \right)\)
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