Q- A mass in the form of a solid cylinder, of radius R acted upon by no forces, moves parallel to its axis through a uniform cloud of fine dust, of volume density ρ, which is at rest. If the particles of dust which meet the mass adhere to it, and if M and u be the mass and the velocity at the beginning of the motion, prove that the distance x traversed in time t is given by the equation

       (M+ρπ R²x)² =M² + 2ρπuR²Mt

Solution: