A) \[\frac{\pi }{2}\]
B) \[\pi \]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{4}\]
Correct Answer: D
Solution :
Key Idea: If \[P\] and \[Q\] are two forces and \[Q\] be the angle between them, then Resultant, \[{{R}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta \] Using the relation \[{{R}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta \] \[\therefore \]\[{{(\sqrt{10}p)}^{2}}={{(2p)}^{2}}+{{(\sqrt{2p})}^{2}}+2(2p)(\sqrt{2p})\cos \theta \]\[\Rightarrow \] \[\cos \theta =\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}\]
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