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sohan singh singh Grade: 12
        


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


7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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

7 years ago
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