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How to find the center of mass of a hemisphere of radius r, with a hole of radius r/2 within it?
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7 years ago

147 Points
```										Dear Amrit pal

dear consider a disk at a distance x of thickness dx whose outer radius is r' and inner radius is r/2
where x2 +r'2 = r2
r' =√(r2 -x2)
mass of the disk dm =ρ (πr'2 -π(r/2)2)dx   where ρ is the dencity
dm =ρπ (r2-x2 -r2/4)dx
dm =ρπ (3r2/4 -x2 )dx
now center of mass = [0∫OC dm *x ]/ o∫OC dm
where OC =√(r2 -(r/2)2)
=r√3 /2
put the value and intigrate
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 preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
7 years ago
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