A ball of mass m attached to a string swings in a vertical circle, as shown. What is the tension in the string when the ball is at the top of the circle?

At the top the forces on the mass are the weight and the tension. Then by Newton's second law we have that the total force Fc is:
[tex]\begin{gathered} F_c=T+mg \\ T=F_c-mg \end{gathered}[/tex]Therefore the answer is b.