Answer:
8.27°
Explanation:
To angle difference will be determined by the difference in the displacement of the springs, produced by the weight of the center of mass of the rod.
[tex]d=y_1-y_2=\frac{F_1}{k_1}-\frac{F_2}{k_2}=\frac{0.5mg}{31N/m}-\frac{0.5mg}{63N/m}\\\\d=0.5(1.6kg)(9.8m/s^2)[\frac{1}{31N/m}-\frac{1}{63N/m}]=0.128m[/tex]
by a simple trigonometric relation you obtain that the angle:
[tex]sin\theta=\frac{d}{l}=\frac{0.128m}{0.89m}=0.144\\\\\theta=sin^{-1}(0.144)=8.27\°[/tex]
hence, the angle between the rod and the horizontal is 8.27°
