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Question: The resultant of two forces \(3P\) and \(2P\)is R. If the first force is doubled then the resultant ...

The resultant of two forces 3P3P and 2P2Pis R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is

A

60o60^{o}

B

120o120^{o}

C

70o70^{o}

D

180o180^{o}

Answer

120o120^{o}

Explanation

Solution

R2=(3P)2+(2P)2+2×3P×2P×cos⁡θR^{2} = (3P)^{2} + (2P)^{2} + 2 \times 3P \times 2P \times \cos\theta …(i)

(2R)2=(6P)2+(2P)2+2×6P×2P×cos⁡θ(2R)^{2} = (6P)^{2} + (2P)^{2} + 2 \times 6P \times 2P \times \cos\theta …(ii)

by solving (i) and (ii),

cos⁡θ=−1/2\cos\theta = - 1/2 ⇒ θ=120∘\theta = 120{^\circ}