Another rotation problem -- Acceleration of a ring rolling on a surface

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The discussion centers on a physics problem involving a rotating ring on a surface, specifically analyzing the acceleration of the center, the frictional force from the ground, and the normal reaction when the ring's geometric center has a velocity of $$ \sqrt{gR} $$. Participants are encouraged to provide their attempts at solving the problem to facilitate guidance. The conversation emphasizes the importance of showing work to receive constructive feedback. The thread also references a related discussion for additional context.
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[Mentors' note - this question was spun off from https://www.physicsforums.com/threa...urface-but-with-a-twist.1078618/#post-7243282 which contains the homework template information]

I'm not sure if I can add on by adding a similar question, if I am not allowed someone please tell me.

A ring is rotating as shown in the figure. At that particular instant when the velocity of the geometric center is $$ \sqrt{gR} $$ find the
1. Acceleration of center
2. Frictional force from ground
3. Normal reaction
 

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palaphys said:
[Mentors' note - this question was spun off from https://www.physicsforums.com/threa...urface-but-with-a-twist.1078618/#post-7243282 which contains the homework template information]

I'm not sure if I can add on by adding a similar question, if I am not allowed someone please tell me.

A ring is rotating as shown in the figure. At that particular instant when the velocity of the geometric center is $$ \sqrt{gR} $$ find the
1. Acceleration of center
2. Frictional force from ground
3. Normal reaction
Where is your attempt?
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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