Magnetic sphere collecting iron dust with force F=k(R³)

[zibs.shirsh]

Homework Statement

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)

Homework Equations

F(external)=0 => ΔP=0
dm = 4∏ρ(R^2)dR

The Attempt at a Solution

couldn;t get any further that writing the above 2 equations

 

[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?