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Two forces whose magnitude are in the ra...

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

Text Solution

Verified by Experts

Let A and B be the two fores.
Then `A=3x, B=5x, R=28 N and theta=60^(@)`
Thus `(A)/(B)=(3)/(5)`
Now `R= sqrt(A^(2)+B^(2)+2Ab cos theta)`
`:. 28= sqrt((3)^(2)+(5x)^(2)+2(3x)(5x)cos 60^(@))`
or `28= sqrt(9x^(2)+25x^(2)+15x^(2))=7x or x=(28)/(7)=4`
`:.` Force are `A=3xx4=12 N and B=5xx4=20 N`
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