Motion in a Circle: True/False/Less/Greater/Equal

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The discussion revolves around the motion of a mass M attached to a string sliding in circles of different radii on a frictionless table. Key points include that M's kinetic energy at the smaller radius is not four times that at the larger radius, contradicting the initial assumption. The angular momentum at the smaller radius is greater than that at the larger radius, while the angular velocity at the smaller radius is not one quarter that at the larger radius. The work done by the force F when moving from the smaller to the larger circle is not zero, and there is no torque acting on M during this transition. Overall, the participants clarify their reasoning for each statement, leading to a consensus on the correct answers.
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Homework Statement


A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of circle (x) is twice the radius of circle (y).
1) M's kinetic energy at y is four times that at x.
2) M's angular momentum at x is ... that at y.
3) M's angular velocity at x is one quarter that at y.
4) As M moves from x to y, the work done by F is ... 0.
5) While going from x to y, there is no torque on M
Each has the options of True/False/Less than/Greater than/Equal to

2. The attempt at a solution
1) False
2) Greater than
3) False
4) False
5) True
 

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Hey, I just saw your other post too. So, same as that one, could you first explain your reasoning for each answer? It helps a lot in seeing if you got the problem right.
 
Nevermind! I was able to get this one as well. My answer turned out to be
1) true
2) equal to
3) true
4) greater than
5) true
 
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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