Forces X,Y and Z have magnitudes `10N`, `5(sqrt(3)-1) N` and `5(sqrt(3)+1) N`, respectively. The forces Y and Z act in the same direction as shown in figure. The resultant of X and Y and the resultant of X and Z have the same magnitudes. Find `theta`, the angle between X and Y.

Options

A. `150^(@)`
B. `135^(@)`
C. `120^(@)`
D. `105^(@)`

Answer

A

Explanation

Resultant of `vec(X)+vec(Y)= vec(X)+vec(Z)`
`(10)^(2)+(5sqrt(3)-1)^(2)+2.10.(5sqrt(3)-1) cos theta`
`=(10)^(2)+(5sqrt(3)+1)^(2)+2.10.(2sqrt(3)+1)cos theta`
or
`(5sqrt(3)-1)^(2)-(5sqrt(3)+1)^(2)`
`=2.10 cos theta[(5sqrt(3)+1)-(5sqrt(3)-1)](2.5.sqrt(3))(-2)= 2.10 cos theta[2]`
`(-5)/(10)sqrt(3)= cos theta = (-sqrt(3))/2`
`= cos thetaimplies theta= 150^(@)`