Question

from the base of a hemisphere a right cone of height r/2 and same base has been snooped out.find the centre of mass of the remaining part

Answer 1

Center of mass of uniform right cone is h/4 from its base where h is it's height .


Center of mass of hemisphere is 3r/8 from its base as shown :




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





Hope it will help you.

Answer 2

Answer:

Explanation:

Center of mass of uniform right cone is h/4 from its base where h is it's height .

Center of mass of hemisphere is 3r/8 from its base as shown :

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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