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Mathematics in Physics

JEE Main level, single correct, medium

35 of 121

Question 35 of 121

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:

Show answer and solution

Answer: (A) ${120}^{^{\circ}}$

\left|\vec{P}\right|=2F,\left|\vec{Q}\right|=3F

\left|\vec{R}\right|=\sqrt{{P}^{2}+{Q}^{2}+2PQcos\theta }

=\sqrt{4{F}^{2}+9{F}^{2}+12{F}^{2}cos\theta }=F\sqrt{13+12cos\theta }

Q

is doubled

2\left|\vec{R}\right|=\sqrt{4{F}^{2}+36{F}^{2}+24{F}^{2}cos\theta }=F\sqrt{40+24cos\theta }

4\left(13+12cos\theta \right)=40+24cos\theta

12=-24cos\theta

cos\theta =-\dfrac{1}{2}

\theta ={120}^{^{\circ}}

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JEE Main 2025 Apr 2 Shift 1 question paper

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JEE Main Physics practice question on Mathematics in Physics (Addition and Subtraction of Vectors), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.

Two forces PPP and QQQ, of magnitude 2F2F2F and 3F3F3F, respectively, are at an angle θ\thetaθ with each other. If the force QQQ is doubled, then their resultant also gets doubled. Then, the angle θ\thetaθ is:

JEE Main question paper PDF

More Physics practice

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: