circular motion physics problem

Question

A rock of mass 200 g is attached to a 0.75 m long string and swung in a vertical plane.

   a) What is the slowest speed that the rock can travel and still maintain a circular path?

   b) What is the tension in the string at the bottom of the swing?

Answer 1

a) Smollest speed it need when at the top tention of spring T = 0, so mg = mv²/l and v = √2gl

v = √2·9.8m/s²·0.75m = 3.834 m/s

b) At lovest point we have: T - mg = mv²/l, T - mg = mg; T = 2mg = 2·0.2kg·9.8m/s² = 3.92 N