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Q.

The resultant of two forces F1 and F2 is F. If F2 is reversed then the magnitude of resultant is 2F. If F2 is doubled then the resultant is also doubled. Find the ratio F1 : F2: F

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a

√3 :√2 :2

b

1: √2 :√3

c

√2 :√3 :√2

d

√3 :2 :1

answer is D.

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Detailed Solution

If the angle between F1 and F2 is θ

Question Image
\large (2F)^2=F_1^2+F_2^2+2F_1F_2cos(\pi-\theta)
\large 4F^2=F_1^2+F_2^2-2F_1F_2cos\theta..................(2)
\large Also , (2F)^2=F_1^2+(2F_2)^2+2F_1(2F_2).cos\theta
\large \Rightarrow 4F^2=F_1^2+4F_2^2+4F_1F_2cos\theta.......(3)
\large Solving , F_1=F,F_2=\frac {\sqrt3.F}{\sqrt2}

Hence, the ratio is 2:3:2

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