A uniform wooden rod (specific gravity = $0.6$, diameter = $4$ $\text{cm}$ and length = $8\:m$) is immersed in the water and is hinged without friction at point $A$ on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = $11.4$) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod.
Assume density of water $ = 10^{3}\:kg/m^{3}$ and $\pi = 3.14$.
Radius of the ball is _____________ $\text{cm}$ (round off to $2$ decimal places).
