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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?


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


Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Amrit pal


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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 = [0OC dm *x ]/ oOC dm

 where OC =√(r2 -(r/2)2)

                =r√3 /2

put the value and intigrate

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Badiuddin

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