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Q.

Two forces of magnitudes P and Q are inclined at an angle (θ) the magnitude of their resultant is 3Q. When the inclination is changed to (180 - θ) the magnitude of theresultant force becomes Q. The ratio of the forces PQ is

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a

41

b

21

c

14

d

12

answer is B.

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Detailed Solution

Case 1 : (3Q)2=P2+Q2+2PQcos⁡θ .............(i)Case 2 : Q2=P2+Q2+2PQcos⁡(180−θ) .............(ii)9Q2=P2+Q2+2PQcos⁡θQ2=P2+Q2−2PQcos⁡θ Adding 10Q2=2P2+2Q2 or 8Q2=2P2 or P2Q2=82=41 or PQ=2

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