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Avijit Arya Grade: 12
`        Can you please solve and show the location of Center of mass for a uniform Hemisphere (both solid and hollow)? Please help me.`
7 years ago

## Answers : (1)

147 Points
```										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
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE  & AIEEE preparation. All the best. Regards,Askiitians ExpertsBadiuddin

```
7 years ago
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