JEE PYQ: Mathematics In Physics Question 24
Question 24 - 2019 (10 Jan Shift 2)
Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle $\theta$ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $\theta$ is:
(1) 120°
(2) 60°
(3) 90°
(4) 30°
Show Answer
Answer: (1)
Solution
Using, $R^2 = P^2 + Q^2 + 2PQ\cos\theta$ $4F^2 + 9F^2 + 12F^2\cos\theta = R^2$ When force Q is doubled, $4F^2 + 36F^2 + 24F^2\cos\theta = 4R^2$ $4F^2 + 36F^2 + 24F^2\cos\theta$ $= 4(13F^2 + 12F^2\cos\theta) = 52F^2 + 48F^2\cos\theta$ $\therefore \cos\theta = -\frac{12F^2}{24F^2} = -\frac{1}{2} \Rightarrow \theta = 120°$
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