2 doubts from Rotational Motion

Doubt 1 : [SOLVED]

A circular disc of radius R has MI equal to I about a perpendicular axis. The radius of the concentric circular part which should be removed so that remaining part has half the MI of disc about the same axis is ?

I tried it by taking MOI of whole disc then subtracting the MOI with distance as x but no answer is matching. Any Hints ?

Options for Doubt 1

A) \frac{R}{2^{\frac{1}{4} } }
B) R/2
C) \frac{r}{\sqrt{2} }
D) \frac{R}{2^{\frac{1}{3} } }

Doubt 2 : [ALMOST SOLVED]

Kinetic energy of a particle moving along a circle of radius r is given by B x^{2} where x is the distance travelled. The resultant acceleration acting on the particle is?

What should be the approach ?

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For the second one…after getting v–> radial velocity, in terms of x and then differentiating it will give tangential acceleration.
Also v²/r is the centripetal acceleration.

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Thank you so much, I’ll try this.

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Did you get the first one?

Not yet

Not yet but I will update here if I get it.

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You must have messed up with the mass of the disk. If we remove some part, mass will also be reduced.

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Ohh I was taking as M only. Let me recheck it now . Thnx for this.

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Thank you @LaveshGupta, it’s done, the error was from mass.

@Amish_1706 Yes, I took a variable as mass per unit area and then while subtracting use that with area as Pie (x)^2 .
If you want I can post the solution here.
Option A is the correct answer.

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Can you post the solution…?

Sure, standby.

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Also, my r and R are same ( small and caps R , are same, please don’t get confused )
Lamda is mass per unit area which remains constant whether we cut the disc or make chips from it.

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Thanks Bro Got it
Actually I was thinking that the perpendicular axis was any arbitrary axis at some distance from the center of the disk because it wasn’t mentioned in the question that it passes from the center. That way I wasn’t able to eliminate one variable.

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Yeah maybe Allen wanted to save space and ink by not specifying about it.
Edit : It’s mentioned Concentric

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:joy: …I don’t think they are that poor

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