Two forces P and Q act such that the resultant R is equal to the magnitude of P. If P is doubled, what is the angle made by the new resultant with the force Q?
A
0∘
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B
30∘
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C
60∘
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D
90∘
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Solution
The correct option is D90∘
R=√P2+Q2+2PQcosθ where θ is the angle between P and Q According to question, P2=P2+Q2+2PQcosθ ⟹Q2+2PQcosθ=0 ⟹Q(Q+2Pcosθ)=0...(1) If α is the angle made by the new resultant with Q then, tanα=2PsinθQ+2Pcosθ Using equ. (1), we can say tanα=2Psinθ0 ⟹α=900