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Two forces whose magnitudes are in the r...

Two forces whose magnitudes are in the ratio `3:5` give a resultant of 28N. If the angle of their inclination is `60^@`, find the magnitude of each force.

Text Solution

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Let A and B be the two forces.
Then `A=3x,B=5x,R=28N` and `theta=60^(@)`.
Dividing A by B,`A//B=3//5`
We know that `R=sqrt(A^(2)+B^(2)+2 AB cos theta)`
`rArr28=sqrt((3x)^(2)+(5x)^(2)+2(3x)(5x)cos 60^(@))`
`=sqrt(9x^(2)+25x^(2)+15x^(2))=7x`
`rArrx=28/7=4`
Hence,forces are `A=3xx4=12N,B=5xx4=20N`.
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