JEE PYQ: Mathematics In Physics Question 15
Question 15 - 2020 (07 Jan Shift 2)
The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $|\vec{R}| = |\vec{P}|$. The angle $\theta$ (in degrees) that the resultant of $2\vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is _____.
Show Answer
Answer: (90)
Solution
Given, $|\vec{R}| = |\vec{P}|$ $P^2 + Q^2 + 2PQ\cos\theta = P^2$ $\Rightarrow Q + 2P\cos\theta = 0$ $\Rightarrow \cos\theta = -\frac{Q}{2P}$ …(i) $\tan\alpha = \frac{2P\sin\theta}{Q + 2P\cos\theta} = \infty$ ($\because 2P\cos\theta + Q = 0$) $\Rightarrow \alpha = 90°$
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