forces due to change in mass I was wondering about if an object experiences a force if its momentum changes on account of change in mass just as momentum of an object changes on applying a force. 
I imagined a table not having friction and a tray having jelly beans sliding over it. Guests sitting along this table would pick these jelly beans without applying a force on the tray.I want to know whether there would be an increase in the velocity  of the tray (considering conservation of linear momentum) or the tray's momentum will decrease with the change in mass and be understood to be in the influence of an imaginary force
 A: The conservation of momentum applies to the entire system.  So it's true that the jar will have less momentum when removing one jelly bean, but that individual jelly bean will still have momentum.  According to the Law of Conservation of Momentum, the total initial momentum of the system = the total final momentum of the system.  Example:
Let's assume the one jelly bean has a mass of 1 g.  The jar has a mass of 5 g.  Let's assume the jar with all its jelly beans was moving at a velocity of 2 m/s, and then while in motion one jelly bean was fell out, so it has a velocity of 2 m/s too:
Initial momentum of system = (5g) (2m/s) = 10g m/s
Final momentum of the system - we have to add up the final momentum of the jar and the jelly bean that fell out:
Jar:  (4g) (2m/s) = 8g m/s
   Bean: (1g) (2m/s) = 10g m/s
Both the initial and final momentum of the system is 10g m/s, so momentum is conserved.
EDIT - I see now that you mentioned the jelly bean would be picked up by a person perpendicularly to the jar's motion.  In this case the Law of Conservation of Momentum does not apply, since there is outside interference.  In this case the person is doing work on the bean, which makes up for the jar's loss of momentum.
A: Assume a body with mass $m+M$ and velocity $\vec{v}_0$ its momentum is given by $\vec{p}_0 = (m+M)\vec{v}_0$: 
If the body losses mass $m$ (assuming instantanously) and the mass $m$ moves with $\vec{v}_0$ then is there no change in momentum according to $\vec{p} = m\vec{v}_0 +M\vec{v}_0= \vec{p}_0$. If it moves in opposite direction (for example: Rocket) then is there a change in momentum by $\vec{p}_{difference} = 2m\vec{v}_0$. Since the momentum is conserved the mass $M$ has to take this momentum and its change is given by: 
$$p (t) = \int_0^t dt' F(t')$$
In this you see that if the momentum changes the derivative $\dot{p}(t) = F(t)$ and $M$ is affected by a force.
A: Indeed, a change of mass can alter the momentum of an object ($\vec{p}=m\vec{v}$). But, if conservation of momentum applies to a system, the velocity of the object will change such that it will cancel the change of mass.
Momentum conservation occurs only if there is no force acting on the object. Here, your example states that someone grabs a jelly bean and thus, an external force is applied on the object. If the force does not act on the tray, then the tray will still move at the same speed (even though the total mass has changed => there is no imaginary force). But, if the tray (somehow) ejects the bean by itself without any external force acting on it, then, momentum is conserved and the speed will change (it will rise) according to the loss of mass.
This is the same principle as a rocket is launched in the air. It pushes (by itself with no external force) burning gas out of its tank at great speed and the loss of mass will push the rocket to liftoff. (see the rocket equation)
