A sphere of mass $M$ and radius $R$ moves with speed $V$ through a region of space that contains particles of mass $m$ that are at rest. There are $n$ of these particles per unit volume. Assume $m$ is very small compared to $M$, and assume that the particles do not interact with each other. What is the drag force on the sphere?
I found this problem in the section of conservation of energy in David morin classical mechanics book.
To address this question I firstly thought of the mechanism by which an ideal gas imposes a dragging Force proportional to velocity gradient owing to internal collisions between the body and the gas molecules. But in this case the main difference is that the spheres of mass m are at rest initially so that this approach simply wont do.
Then this idea came to my mind that the body,as it propagates through the medium creates spherical waves in that medium just like the pressure waves in ideal gas and if this is the case then the drag force must be proportional with the acoustic pressure at the region where the body lies.As the position of the body is not fixed,say,at position A it created a spherical wave and now the body has reached point B and at point B the drag force should be according to my logic equal to the acoustic pressure due to the wave which it created while it was it at point A. Now I am failing to mathematically model this idea to turn it into an answer to the question. How can i do this?