# Rolling all the way down

A hollow sphere has a light rope wound over it. The end of the rope is attached to a rigid support which is at a height $$h$$ from the surface of the earth, It acquires the same velocity just before touching the ground as that acquired by a free falling body under gravity from a height $$h'$$ from the surface of the earth.If $$R_{e}$$ is the radius of the earth, what is the value of $$R_{e} [\dfrac{3}{h'} - \frac{5}{h} ]$$?

Details and Assumptions:

• Radius of sphere is very much smaller than radius of earth

• Consider the variation of acceleration due to gravity with height as both $$h$$ and $$h'$$ are quite large

• The rope doesnt slip on the sphere.
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