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"


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