Statement-I : Two forces P → + Q → and P → - Q → where P → ⊥ Q → , when act at an angle θ 1 each other, the magnitude of their resultant is 3 P 2 + Q 2 , when they act at an angle θ 2 , the magnitude

Question

Statement-I : Two forces P → + Q → and P → - Q → where P → ⊥ Q → , when act at an angle θ 1 each other, the magnitude of their resultant is 3 P 2 + Q 2 , when they act at an angle θ 2 , the magnitude of their resultant becomes 2 P 2 + Q 2 . This is possible only when θ 1 < θ 2 . Statement-II : In the situation given above. θ 1 = 60 ° and θ 2 = 90 ° In the light of the above statement, choose the most appropriate answer from the options given below :

TestHub · Accepted Answer

F → 1 and F → 2 at θ 1 F n e t 1 = P 2 + Q 2 + P 2 + Q 2 + 2 P 2 + Q 2 cos θ 1 F n e t 2 = P 2 + Q 2 + P 2 + Q 2 + 2 P 2 + Q 2 cos θ 2 If F n e t 1 = 3 P 2 + Q 2 = 2 P 2 + Q 2 + 2 P 2 + Q 2 cos θ 1 ⇒ cos θ 1 = P 2 + Q 2 2 P 2 + Q 2 ⇒ θ 1 = 60 ° F n e t 2 = 2 P 2 + Q 2 = 2 P 2 + Q 2 + 2 P 2 + Q 2 cos θ 2 ⇒ cos θ 2 = 0 ⇒ θ 2 = 90 °

Physics - Vectors Question with Solution | TestHub

Options:

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