Two forces P and Q are in ratio `P:Q=1:2`. If their resultant is at an angle `tan^(-1)((sqrt3)/(2))` to vector P, then angle between P and Q is :

Options

A. `tan^(-1)((1)/(2)) `
B. `45^(@) `
C. `30^(@)`
D. `60^(@)`

Answer

A

Explanation

`tan alpha =(Q sin theta)/(P+Q cos theta) `
`sqrt(3)/2 =(sin theta )/((P)/(Q)+cos theta ) rArrsqrt(3)/(2) =(sin theta )/((1//2)+cos theta ) rArr (3)/4=((2 sin theta )/(1+2 cos theta ))^(2)`
`rArr 3(1+2 cos theta )^(2)=16 sin ^(2) theta `
`rArr 3(1+4cos^(2) theta +4cos theta)= 16(1-cos ^(2) theta)`
`rArr3+12cos ^(2) theta +12 cos theta =16-16 cos ^(2) theta`
`rArr 28cos^(2)theta +12 cos theta -13=0 rArr " " cos theta = (1)//(2), -0.92`