Can you please solve and show the location of Center of mass for a uniform Hemisphere (both solid and hollow)? Please help me.
Dear Avijit
The volume of a hemisphere is 2pR3/3.
The density of the hemisphere r =
Mass/volume = M/(2pR3/3) = 3M/2pR3.
In Fig above, the volume of an element dV = px2 dy.
The mass of the element dm =
rdV = (3M/2pR3)px2 dy.
Notice that x2 = R2 - y2 and that dm = (3M/2pR3)p(R2 - y2) dy.
now for center of mass intigrate
C.O.M = ∫ydm/M limit 0 to R
put the value of dm and perform intigration you will get
C.O.M = 3R/8
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Badiuddin
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