Inelastic collision involving pulley

[issacnewton]

Here is the problem I am trying

Two blocks A and B of same mass M are connected with
each other with an ideal string of length $2l$ passing over an
ideal pulley. The block A is connected to a light pan C
with an ideal string as shown in figure. A particle of mass
$\frac{M}{2}$ is dropped on pan from height
$\frac{l}{2}$ as shown. If
collision between particle and pan is plastic, acceleration
of B just after the collision is

a) $g$

b) $\frac{g}{9}$

c) $2g$

d) none of above

I have attached the snapshot of the problem. Now, I am thinking on the following lines. Since
the pan is light, when the mass M/2 falls on it, the string attached to the pan will feel the jerk.
And we can think of mass M/2 attached to the pan and accelerating downwards with acceleration g. Do you think this is a good starting point ? I am not sure if my reasoning is correct here...

thanks

 

[haruspex]

Since
the pan is light, when the mass M/2 falls on it, the string attached to the pan will feel the jerk.
And we can think of mass M/2 attached to the pan and accelerating downwards with acceleration g.

You don't think the pan and attached masses will reduce the acceleration at all?
Try doing the free body diagrams for the three masses when M/2 has reached the pan.

 

[Saitama]

You don't think the pan and attached masses will reduce the acceleration at all?
Try doing the free body diagrams for the three masses when M/2 has reached the pan.

I don't know if IssacNewton is willing to continue the thread but I would like to understand how to solve this. How did the OP conclude that the acceleration of the pan is g, is this even correct? Basically, how should I approach this problem?

 

[issacnewton]

Sorry for late reply. I thought that since falling mass is going to hit the pan, its acceleration would be g. Probably this is wrong.

 

[haruspex]

I thought that since falling mass is going to hit the pan, its acceleration would be g. Probably this is wrong.

It's g before it hits the pan of course, but that's not what we want to know.
This is rather a curious problem. I don't know whether it intends to confuse by supplying irrelevant information, but it certainly does that.
It asks for the accelerations just after hitting the pan, not the velocities. So here's a question: do the velocities immediately after impact affect the forces at that time? If not, the history doesn't matter: we can just look at the free body diagram after impact, and not even care that an impact occurred.