In our discussion of the conservation of linear momentum, we have so far deal with object whose mass keeps constant. We now take those systems whose mass is not fixed, i.e., those in which mass leaves or enters the object. A typical case is that of the rocket from which hot gases remain on escaping, thereby continuously decreasing its mass.

In such problems you have nothing to do but give a thrust force  to the main mass in addition to the all other forces performing on it. This thrust force is shown as,

The expression for the thrust force can be provided from the conservation of linear momentum in the absence of any external forces on a object as follows:

Consider at some moment t = t mass of a object is m and its velocity is . After some time at t = t + dt its mass goes (m = dm) and velocity becomes . The mass dm is ejected with relative speed  , Absolute velocity of mass 'dm' is therefore . If no external forces are operating on the system, the linear momentum of the system will keep conserved,

Or                          

Or                                   

Or                     

Here,              

And     

Problems related to variable mass may be answered in following three steps:

1. Create a list of all the forces performing on the main mass and apply them on it.

2. Apply an additional thrust force on the mass, the value of which is  and direction is given by the direction of in case the mass is increasing and otherwise the direction of -if it is decreasing.

3. Find net force on the mass and apply

                 (m = mass at that particular instant)

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