JEE MAIN - Physics (2019 - 10th January Evening Slot - No. 15)
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 -
90o
60o
30o
120o
Explanation
4F2 + 9F2 + 12F2 cos $$\theta $$ = R2
4F2 + 36F2 + 24F2 cos $$\theta $$ = 4R2
4F2 + 36F2 + 24F2 cos $$\theta $$
= 4(13F2 + 12F2cos$$\theta $$) = 52F2 + 48F2cos$$\theta $$
cos $$\theta $$ = $$-$$ $${{12{F^2}} \over {24{F^2}}}$$ = $$-$$ $${1 \over 2}$$
4F2 + 36F2 + 24F2 cos $$\theta $$ = 4R2
4F2 + 36F2 + 24F2 cos $$\theta $$
= 4(13F2 + 12F2cos$$\theta $$) = 52F2 + 48F2cos$$\theta $$
cos $$\theta $$ = $$-$$ $${{12{F^2}} \over {24{F^2}}}$$ = $$-$$ $${1 \over 2}$$
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