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 the
resultant force becomes Q. The ratio of the forces $(\frac{P}{Q})$ is

Question

Infinity Learn · Accepted Answer

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

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 the
resultant force becomes Q. The ratio of the forces $(\frac{P}{Q})$ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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 the
resultant force becomes Q. The ratio of the forces $(\frac{P}{Q})$ is