Answer to Question #232414 in Mechanical Engineering for Surya bhai

Question

The resultant of two forces 3P and 2P is R if the first force is doubled then the resultant is also doubled. the angle between the two forces is 

A

60∘

B

120∘

C

70∘

D

180∘

Answer 1

$Solve \space two \space equation :\\ R ^ 2 =9P ^2 +4P^ 2 +12P^ 2 cosθ=13P^ 2 +12P^ 2 cosθ .....(1)\\ (2R)^ 2 =(2×3P) ^2 2 +4P^ 2 +24P^ 2 cosθ=40P ^2 +24P^ 2 cosθ ....(2)\\ Multiplying (1) \space by \space 4, 4R^ 2 =52P^ 2 +48P^2 2 cosθ .....(3)\\ Equating \space (2) \space and \space (3)\\ 40P ^ 2 +24P^ 2 cosθ=52P ^ 2 +48P^ 2 cosθ\\ ⇒12P^ 2 =−24P^ 2 cosθ\\ ⇒cosθ=− 2 1 ​ =cos120^ ∘\\ ⇒θ=120^ ∘$