Problem Solving: Input your final answer in the space provided.

Note: Use four $(4)$ decimal places and no need to indicate the unit.

A yellow pine $\backslash (\backslash$operatorname$\{$rod$\}(\backslash$mathrm$\{$SG$\}=0\mathrm{.}65\backslash ))$ is $10$ cm by $10$ cm by $2\mathrm{.}2$ m long. How much weight of lead in $\backslash (\backslash$mathrm$\{$N$\}(\backslash$mathrm$\{$SG$\}=\backslash )11\mathrm{.}4$ is needed at one end so that the rod will float vertically with $37$ cm out of the water?