$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

• A
  $\frac{h}{l}=\frac{\sqrt{3}}{16}, f=\frac{16 \sqrt{3}}{3} \,N$
• B
  $\frac{h}{l}=\frac{3}{16}, f=\frac{16 \sqrt{3}}{3} \,N$
• C
  $\frac{h}{l}=\frac{3 \sqrt{3}}{16}, f=\frac{8 \sqrt{3}}{3} \,N$
• D
  $\frac{h}{l}=\frac{3 \sqrt{3}}{16}, f=\frac{16 \sqrt{3}}{3} \,N$