A) \[30\sqrt{7}\]
B) \[30\sqrt{3}\]
C) \[20\sqrt{6}\]
D) \[25\sqrt{2}\]
Correct Answer: A
Solution :
Key Idea Resultant of two forces \[P\] and \[Q\] making an angle \[\alpha \] with each other, is \[R=\sqrt{{{P}^{2}}+{{Q}^{2}}+2PQ\cos \alpha }\] Since, forces of magnitude \[30,\,\,60\] and \[P\] are in equilibrium, then magnitude of \[P\] is equal to the magnitude of resultant of forces of magnitude \[30\] and\[60\]. \[\therefore \] \[P=\sqrt{{{(30)}^{2}}+{{(60)}^{2}}+2(30)(60)\cos {{60}^{o}}}\] \[=\sqrt{900+3600+3600\times \frac{1}{2}}\] \[=\sqrt{4500+1800}=\sqrt{6300}\] \[=30\sqrt{7}\]
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