Answers:
a) 
b) 
Explanation:
a) The centripetal acceleration  of an object moving in a uniform circular motion is given by the following equation:
 of an object moving in a uniform circular motion is given by the following equation:  
 
  
Where:
 is the angular velocity of the ball
 is the angular velocity of the ball
 is the radius of the circular motion, which is equal to the length of the string
 is the radius of the circular motion, which is equal to the length of the string
Then:
 
  
 This is the centripetal acceleration of the ball
 This is the centripetal acceleration of the ball
b) On the other hand, in this circular motion there is a force (centripetal force  ) that is directed towards the center and is equal to the tension (
) that is directed towards the center and is equal to the tension ( ) in the string:
) in the string:

Where  is the mass of the ball
 is the mass of the ball
Hence:

 This is the tension in the string
 This is the tension in the string