Doubt from rotation

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For 9 apply conservation of energy

little weak at rotation can you send the solution please @Achyut_2020

MgR=(M/4)g(R/2)+(1/2)(M/4)v^2+(1/2)(M/4)(R/2)^2 w^2
Now solve it put v=wR/2
As work done by friction and normal force will be zero
If not understood ,let me know

Question 9 is a ncert question or sl arora book question if you have it you can check it

Question 8 Option A

You can place region 1 in region 2 moment of inertia of systen still wont same.
Regarding question 9 it came in IITJEE.

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I gave given this paper but this question is a ncert question so i don't remember ncert but students who follow ncert remember these questions

Got it .Thanks guys.

Since it is a rolling motion, wd by friction will be zero