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Question

Physics Question on Newtons Laws of Motion

Two forces PP and QQ of magnitude 2F2F and 3F3F, respectively, are at an angle θ\theta with each other. If the force QQ is doubled, then their resultant also gets doubled. Then, the angle is :

A

30 30^{\circ}

B

60 60^{\circ}

C

90 90^{\circ}

D

120 120^{\circ}

Answer

120 120^{\circ}

Explanation

Solution

4F2+9F2+12F2  cos  θ=R24F^2 + 9F^2 + 12F^2 \; \cos \; \theta = R^2
4F2+36  F2+24  F2  cos  θ=4R24F^2 + 36 \; F^2 + 24 \; F^2 \; \cos \; \theta = 4R^2
4F2+36  F2+24  F2  cos  θ4F^2 + 36 \; F^2 + 24 \; F^2 \; \cos \; \theta
=4(13F2+12F2cosθ)=52  F2+48F2cosθ= 4(13F^2 + 12F^2 \cos \theta) = 52 \; F^2 + 48F^2 \cos \theta
cosθ=12F224F2=12\cos \theta = \frac{12 F^2}{24 F^2} = - \frac{1}{2}