Question

Two forces of magnitude P and Q are inclined at an angle theta, the magnitude of their resultant is 3Q. When the inclination is changed to 180-theta the magnitude of the resultant force becomes Q .the ratio of their p/q is

Answer 1

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$\Huge{\red{\underline{\textsf{Answer}}}}$

$\frac{P}{Q}$ = 2

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$\large{\green{\underline{\tt{Solution}}}}$

$\hookrightarrow$( 3Q² ) = P² + Q² + 2PQ cos$\emptyset$

$\hookrightarrow$Q² = P² + Q² + 2PQ cos$\emptyset$( 180° - $\emptyset$ )

$\hookrightarrow$9Q² = P² + Q² + 2PQ cos$\emptyset$

$\hookrightarrow$10Q² = 2P² + 2Q²

$\hookrightarrow$8Q² = 2P²

$\hookrightarrow$$\frac{P}{Q}$ = $\frac{8}{3}$ = $\frac{4}{1}$

$\hookrightarrow$$\frac{P}{Q}$ = 2

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