# Tension for the crown

The blacksmiths of the kingdom of Mechania are wondering how much tension is holding a crown together as it rests on the head of their sovereign. The king of Mechania has a frictionless, perfectly spherical head with radius $$r = 10 \text{ cm}$$, and the crown is a thin cord with a length of $$\ell = 37.7 \text{ cm}$$ and a mass of $$m = 628.32 \text{ g}.$$

Compute the tension in the crown (in Newtons).

Assumptions:

• The crown has no thickness and rests perfectly level (that is, it makes a circle which is contained in a plane parallel to the horizontal).
• The gravitational constant of Mechania is $$g = 10 \text{ m/s}^2.$$
×