Finding center of mass of a round-bottomed cone by combining a cone and hemisphere

[Gogsey]

Is there anyway of breaking up the parts of an a round spherical bottomed cone into a regular cone and a hemisphere?

I can find the CM of a cone with its tip on the origin, and a hemisphere with its flat bottom in the x-y plane. Can I break the round bottomed cone up into these 2 parts? How would I go about combining them to find the CM of the round bottomed cone?

The z-axis goes though the centre of the round bottomed cone lengthways.

 

[chrisk]

Yes, superposition can be used to find the CM of the object. Find the CM of the hemisphere then find the CM of the cone using a common coordinate system. These two locations can treated as point masses then be used to find the CM of the object.

 

[Gogsey]

Does that mean I can but the flat bottom of the hemisphere at the origin, and the tip of the cone at the origin? Or do I have to put say the cone tip at the origin, and the flat bottom of the hemisphere at the top of the cone?

So then how do I find the combined CM for the object?

 

[chrisk]

It does not matter where you place the origin but a convenient location would be where the cone and hemisphere meet and intersect with the line of symmetry. To answer your second question, how would you find the CM of two point objects?