Question

when two forces of magnitude P and Q are perpendicular to each other, their resultant is of magnitude R. when they are at angle of 180° each other their resultant is of magnitude R/(g2^1/2). find the ratio of P and Q

Answer 1

Answer:

P/Q  = (√3 + 1)/(√3 - 1)  = 2 + √3

Explanation:

when two forces of magnitude P and Q are perpendicular to each other, their resultant is of magnitude R. when they are at angle of 180° each other their resultant is of magnitude R/(2^1/2). find the ratio of P and Q

two forces of magnitude P and Q are perpendicular to each other,

=> Resultant Magnitude = R = √(P² + Q²)

Squaring both sides  R² = P² + Q²

when they are at angle of 180° each other their resultant = P - Q

P - Q  =  R/ √2

Squaring Both Sides

=> P² + Q² -2PQ = R²/2

=> R² - 2PQ = R²/2

=> 2PQ = R²/2

P² + Q² = R²

=> (P + Q)² - 2PQ = R²

=> (P + Q)² = R² + R²/2

=>  (P + Q)² = 3R²/2

=> P + Q = √3R/√2

Adding both

2P = (R/√2)(1 + √3)

2Q = (R/√2)(√3 - 1)

P/Q  = (√3 + 1)/(√3 - 1)  = 2 + √3