# The Speck Of Dust Returns

**Classical Mechanics**Level 5

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"