# Hemisphere center of mass

1. Mar 30, 2015

### Westin

1. The problem statement, all variables and given/known data
Consider a solid hemisphere of uniform density with radius R. Where is the center of mass?

z=0
0 z R 2
z=R 2
R 2 z r
z=R

Image is provided.

2. Relevant equations

None

3. The attempt at a solution

Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of mass is the average of the masses factored by their distances from a reference point. I didn't think the answer could range like B and D do.

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Last edited by a moderator: Apr 16, 2017
2. Mar 30, 2015

### Staff: Mentor

Really? No equation for the center of mass?

Do you understand that the range is there to keep you from having to calculate the exact value? It doesn't mean that the center of mass can be anywhere within that range.

3. Mar 30, 2015

### NTW

If the center of mass were precisely at R/2, there will be more mass below than above that point. Hence, it must be somewhere between R/2 and...

4. Mar 30, 2015

### Staff: Mentor

I don't understand what you mean.

5. Mar 30, 2015

### NTW

To make a mental experiment: If I imagine a given point on the Z axis, precisely at R/2, and also imagine the hemisphere as formed by a very large, but finite number of particles, the number of particles with z-coordinates lower than R/2 will be larger than the number of particles with z-coordinates higher than R/2. Hence, in order to reach a 50% partition in the values of the z-coordinates, that point must be placed somewhere between 0 and R/2.

6. Mar 30, 2015

### Staff: Mentor

Ok, but that's not the same as saying "if the center of mass were precisely at R/2."

Also, please to not give direct answers in the homework forums. The poster has to do the work.