# Magnetic sphere moving through iron dust; find velocity & other things

1. Oct 1, 2013

### zibs.shirsh

1. The problem statement, all variables and given/known data
A small magnetic sphere of initial mass Mo and initial radius Ro is moving through a space filled with iron dust. During its motion, 5% of displaced dust is deposited uniformly onto the surface of sphere. Given the density of dust to be ρ, find:
1. relation rate of increase in radius and velocity
2. if the magnet is moving under a force F=k(R^3), along the direction of motion, obtain a differential equation for radius at time t, when mass at time t, is much greater than it's initial mass and radius much greater that it's initial value
3. assuming a particular solution of differential equation to be R=b(t^2), find the value of acceleration of magnet ball at time t.

(b,k are constants)

2. Relevant equations
F(external)=0 => ΔP=0
dm = 4∏ρ(R^2)dR

3. The attempt at a solution
couldn;t get any further that writing the above 2 equations

Last edited: Oct 1, 2013
2. Oct 1, 2013

### haruspex

your second equation doesn't make sense dimensionally. The LHS is M/T while the right is just M.
Suppose the ball is moving at speed v = v(t). How much dust is displaced in time dt? So how much is deposited, and how much does the radius increase by?