Conservation of momentum in a mechanics problem

[eli meril]

Homework Statement

I solved the first section.
The second section true I think.
I solved but I want you to tell me that .
And the other sections that I do not already know how to solve them, if someone can target me?

Homework Equations

in the poto 2-5.
but 5 and 4 less relevant that the others .

The Attempt at a Solution

at section 2 Conservation of momentum .
I have doubts about the little mass to be considered

 

[andrevdh]

Hint: The bead accelerates along the "rainbow" portion.

 

[eli meril]

It's does not help me so mach.
I do not know if you refer to the circle or do simple momentum conservation.

 

[eli meril]

It's does not help me so mach.
I do not know if you refer to the circle or do simple momentum conservation.

 

[haruspex]

The second section true I think.
I solved but I want you to tell me that .

Please post your solution and working. Use only the symbolic names given (m, M etc.); please do not substitute any numerical values.

 

[andrevdh]

So do you need help with question number 3?
If you want to know if your answers for 1 and 2 is correct you need to post your solution here.