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  4. At what angle should the two forces 2P and √2P act so that the resultant force is ? P√10

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Q. At what angle should the two forces $2P$ and $ \sqrt{2}P $ act so that the resultant force is ? $ P\sqrt{10} $

AFMCAFMC 2010

Solution:

Resultant, $R=\sqrt{A^{2}+B^{2}+2 A B \cos \theta}$
$P \sqrt{10}=\sqrt{4 P^{2}+2 P^{2}+4 \sqrt{2} P^{2} \cos \theta}$
$ \therefore \theta=45^{\circ}$