1998 5 marks

A cylindrical solid of mass 10-2 kg and cross-sectional area 10-4m2 is moving parallel to its axis (the x-axis) with a uniform speed of 103m/s in the positive direction. At t = 0, its front face passes the plane x = 0. The region to the right of this plane is filled with stationary dust particles of uniform density 10-3  kg / m3 . When a dust particle collides with the face of the cylinder, it sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged and that the dust sticks only to the front face of the cylinder find the x-coordinate of the front of the cylinder at t = 150 s.

Momentum conservation doesn't apply here. Ignore the stupid solutions and try your own.