A perfectly symmetrical tree has a trunk in the shape of a cylinder with diameter \(0.2~\mbox{m}\). Since the tree is symmetrical the center of mass is at some distance \(L\) above the ground along the axis of the cylinder. A rotten lumberjack with no concept that he's cutting down the most amazing tree ever grown uses a chain saw to cut the tree down. He saws horizontally right at the base of the tree (ground level).

What is the minimum value of \(L\) **in meters** such that the tree begins to topple over as soon once the chain saw reaches the position in the picture?

**Details and assumptions**

- The chain saw blade is \(8~\mbox{cm}\) wide and \(0.5~\mbox{cm}\) high.
- Treat the tree as a rigid body.

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