Another Doubt From Halliday Resnick Krane -- Puck on a string in circular motion

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A puck on a frictionless table moves in a circular path due to a string attached to a hanging mass. The hanging mass creates tension in the string, which provides the necessary centripetal force for the puck's circular motion. An initial push is required to set the puck in motion, after which a steady state can be achieved without friction. The system relies on the balance between gravitational force on the hanging mass and the tension needed for circular motion. Understanding this relationship clarifies how the setup operates in a frictionless environment.
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Hello! This is a problem from Halliday Resnick Krane (Chapter 4: Problem #15). “A puck is moving in a circle of radius r0 with a constant speed v0 on a level frictionless table. A string is attached to the puck, which holds it in the circle; the string passes through a frictionless hole and is attached on the other end to a hanging object of mass M.” What I don’t understand is how this system works. How does hanging a heavy mass through a table make the mass m on the table spin in a circle?
 
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Someone has given it an initial push sideways to make it circle as described. After a small time, absent friction, a steady state can ensue.
 
The weight of the mass M causes tension in the string. The tension then acts as the centripetal force required for circular motion. As @hutchphd mentioned an initial push is required to start the circular motion.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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