Calculate the Angle Between The Two Forces, If The Resultant Force Gets Doubled When The First Force is Doubled

R2 = (3P)2 + (2P)2 + 2(3P)(2P) cosӨ

R2 = 13P2 + 12P2 cosӨ Equation 1

It is given that, when the first force is doubled, the resultant force also gets doubled. Therefore,

(2R)2 = (6P)2 + (2P)2 + 2(6P)(2P) cosӨ

4R2 = 40P2 + 24P2 cosӨ Equation 2

Subtracting equation (2) from (1),

4R2 – 4R2 = 52P2 + 48P2 cosӨ – 40P2 – 24P2 cosӨ

0 = 12P2 + 24P2 cosӨ

cosӨ = -½

Ө = 120°

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