# Variable Mass and Conservation of Linear Momentum

The problem is related to variable mass systems. A cylinder is moving through dust particles and the particles are sticking to it.

A mass in the form of a solid cylinder, of radius c acted upon by no forces, moves parallel to its axis through a uniform cloud of fine dust, of volume density , 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

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The solution file is attached.

Solu. Mass of the system moving at any time t is the mass of the cylinder and the mass of the dust deposited on the front plane surface of the cylinder, therefore this is the case of variable mass system and the mass of the system as a function of time is given by

where x is the distance traversed by the cylinder in time t.

If in an infinitesimal time dt it covers a distance dx (velocity dx/dt), according to law of conservation of linear momentum

Integrating

Substituting value of in LHS of given equation we have RHS

© BrainMass Inc. brainmass.com October 5, 2022, 2:58 pm ad1c9bdddf>https://brainmass.com/physics/conservation-of-momentum/variable-mass-conservation-linear-momentum-34175