Two force in the ratio `1:2` act simultaneously on a particle. The resultant of these forces is three times the first force. The angle between them is

Options

A. `0^(@)`
B. `60^(@)`
C. `90^(@)`
D. `45^(@)`

Answer

A

Explanation

Let `vecF_1 and vecF_2` be the two forces acting on a particle simultaneously and ..be the angle between them.
The resultant of these two forces is
`R = sqrt(F_1^2+F_2^2+2F_1F_2cos theta)" "...(i)`
Acooding to question
`F_1/F_2=1/2" or " F_2=2F_1`
and `R = 3F_1`
Substituting these values in equation (i) ,we get
`(3F_1)^2=F_(1)^(2)+(2F_(1))^2+4F_(1)^(2)cos theta`
or ` 4 cos theta = 4 " or " cos theta=1`
or ` theta = cos ^(-1)(1) =0^(@)`