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Can you please solve and show the location of Center of mass for a uniform Hemisphere (both solid and hollow)? Please help me.

Can you please solve and show the location of Center of mass for a uniform Hemisphere (both solid and hollow)? Please help me.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Avijit


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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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Regards,
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Badiuddin



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