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ANSWER :-
a)
Given,
The disc is initially in rest
So energy stored at top is potential energy = mgh
When the disc comes down and joins the block , the combined mass forms a system with combined mass (m+M)
Let's assume this combined mass have attained a velocity "v"
So, the Kinetic energy gained by the combined system is
Now coming to the point , work done
WORK DONE :-
Work done by friction is defined as change in the total energy of the body(system)
b)
And coming to the second part of the question,
Here the body comes into rest due to friction and there is a no question of non inertial frame of reference for the above phenomenon
So I think it doesn't change.
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