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 between Q. The ratio of the forces (PQ) is

Question

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 between Q. The ratio of the forces (PQ) is

Infinity Learn · Accepted Answer

(3Q)2$$ $$=$$ $$P2+Q2+2PQcos$$θ$$9Q2$$ $$=$$ $$P2+Q2+2PQcos$$θ$$------(i)Also$$, $$Q2$$ $$=$$ $$P2+Q2+2PQcos$$θ$$(180-$$θ$$)Q2$$ $$=$$ $$P2+Q2-2PQcos$$θ$$----(ii)Adding$$ $$(i) and (ii), $$10Q2$$ $$=$$ $$2P2+2Q2or$$ $$8Q2$$ $$=$$ $$2P2or$$ $$P2Q2$$ $$=$$ $$82=$$ $$41$$     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 between Q. The ratio of the forces ( $\frac{P}{Q}$ ) is

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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 between Q. The ratio of the forces (PQ) is

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