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from the base of a hemisphere a right cone of height r/2 and same base is scooped out then centre of mass of remaining part is

from the base of a hemisphere a right cone of height r/2 and same base is scooped out then centre of mass of remaining part is

Grade:12th pass

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
3 years ago
Center of mass of uniform right cone is h/4 from its base where h is it's height .

In this case h =r/2,so h/4=r/8.

We can assume uniform density and use the concept of negative mass. From symmetry.We know that center of mass must lie on the Y axis .


Volume of hemisphere=(π.r cube ) .2/3
Volume of cone=(π.r square .r/2)/3=
(π.r cube)(1/6)

Center of mass =(2/3*3r/8-1/6*r/8)/2/3-1/6)
=(11/24)r

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