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  4. When two equal forces are inclined at an angle 2 α, their resultant is twice as great as when they act at an angle 2 β, then

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Q. When two equal forces are inclined at an angle $2 \alpha$, their resultant is twice as great as when they act at an angle $2 \beta$, then

Bihar CECEBihar CECE 2013

Solution:

Let the magnitude of each force be $P$.
Then, $R_{1}=$ Resultant of two equal forces each of magnitude $P$ inclined at an angle $2 \alpha=2 P \cos \alpha$, and
$R_{2}=$ Resultant of two equal forces each of magnitude $P$ inclined at an angle $2 \beta=2 P \cos \beta$
It is given that, $R_{1}=2 R_{2}$
$\Rightarrow 2 P \cos \alpha=4 P \cos \beta$
$\Rightarrow \cos \alpha=2 \cos \beta$