# The Speck Of Dust Returns

A speck of dust of negligible mass begins to fall under gravity through a region of space with saturated water vapor. If the mass accumulation is B times the instantaneous surface area of the drop, calculate the acceleration of the drop in $$\text{ms}^{-2}$$.

Details and Assumptions

• The drop falls through uniform gravitational field where $$g= 10\text{ ms}^{-2}$$.
• Assume the drop to be spherical.

• B is a constant

Hint: If $$r$$ is the radius of the drop, show that $$\dfrac{dr}{dt}$$ is proportional to $$B$$.

this problem is part of the set "innovative problems in mechanics"

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