Doubt from Rotational motion

Getting D

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Well is there any chance of solving it without integration ?

Yeah, it's really easy by parallel axis therom...

Yes if you have learned M.I. through some other axis also

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Thanks @Abhishek_2020_5 this is what I want . I considered Icom = Mh^2/6 directly silly mistake.

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Conceptual doubt

It should be C....

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And is C according to me this is possible only if friction is sufficient to prevent slipping , please correct me if I am wrong

Frictional force is not required as torque of F itself will provide sufficient angular acceleration to avoid slipping

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Can you please explain how?

F. R=mR^2α....(1) there is no torque due to gravity and normal reaction.
F+f=ma....(2)
a=α×R.....(3) essential condition for pure rolling.
Put value of α in equation (1) and compare it to (2).
You get f=0
This is not intial case. It happens after some time.

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This case starts when V_{cm}=\omega ×R

Yeah, that what I am saying so don't you think that this question is incomplete

Ya, they should have mentioned that

https://www.toppr.com/ask/question/a-ring-of-mass-kept-on-a-horizontal-rough-a-force-f-is-applied-tangentially/
#see this