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No sure but the answer should be either h or 0.

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So, the ball was not dropped vertically

Nope...and sorry i Forgot to Draw the Pic !

Yup...

But The answer shuld be 2h/3 ....No prob...Show the Way u Did This..)

Velocity at Bottom is sqrt 2gh

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So..According to u h =h1

i mean vg' is not equal to 0...,

Ball is on Translation..)

Not need to Consider Moment of Inertia

The answer shuld be 2h/3

If there is no friction...then I suppose the height should be halved...

i also got the ans as h/2. wonder where i'm going wrong....is the ans really 2h/3 ?

It's H/2. Recheck your solutions.