# Alokananda's Sand Tower

Directly below her $$10\text{ m}$$ tall tower, Alokananda has piled up a heap of sand $$1\text{ m}$$ high.

When she drops a ball of density $$\rho$$ from the top of the tower, the ball does reach the bottom of the sand (whose density, by the way, is $$\sigma$$) pit, but by then, it is completely exhausted of its kinetic energy.

Modelling the heap of sand as a pool of fluid and assuming that the Archimedes' principle is the only reason for the resistance provided by the sand, what is the value of $$\dfrac{\sigma}{\rho}$$?

Assume that the ball has a positive radius negligible compared to the height of fall. Further, also assume that the ball immerses completely and no energy is lost in the air-sand transition.

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