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P and Q are two forces of equal magnitude acting at a point O at such an angle that their resultant R has a magnitude equal to that of P . If the magnitude of P is doubled then find the angle between the new resultant R1 and Q. |
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Answer» Explanation: Here P , Q and R in magnitude are equal according to the question, So, we can write, R^2 = P^2 + Q^2 + 2PQcos thetaP^2 = P^2 + P^2 + 2P^2 cos theta [Acc. to the question]After solving,-1/2 = cos thetacos 120 = cos thetaTherefore, theta = 120Again, the new angle between R1 and Q be ∅ when P is doubled is, We have from Parallelogram LAW, Tan∅ = Tan∅ = 2Q sin 120 / 2Q + Qcos 120After PUTTING theta value we get, Tan∅ = ∞Therefore,∅ =90 degree. |
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