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.

Options

A. `1N` `2N`
B. `12N` `20N`
C. `12N` `12N`
D. `22N` `20N`

Answer

B

Explanation

Let A and B be the two forces ,then `A=3x,B=55x
`R=28N and `theta=60^(@)`
thus , `(A)/(B)=(3)/(5)`
Now,`R=sqrt(A^(2)+B^(2)+2ABcostheta)`
`28= sqrt((3x)^(2)+(5x)^(2)+2(3x)+(5x)cos60^(@))`
`28sqrt(9x^(2)+25x^(2)+15x^(2)=7xor x=4)`
`F_(A)=3xx4=12N and B=5xx4=20N`