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A top (plumb line) can be construed by joining cone of radi R and height R and a hemisphere of radi R of uniform density. Distance of com from common centre is

A top (plumb line) can be construed by joining cone of radi R and height R and a hemisphere of radi R of uniform density. Distance of com from common centre is

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
COM of the cone =C1=(0,R/3)
COM of the hemisphere =C2=(0,3R/8)
Volume of the cone=V1= πR3/3
Volume of the hemisphere=V2=2πR3/3

COM on the y-axis of the system
=(C1V1+C2V2)/(V1+V2)
=((R/3 x πR3/3)+(3R/8 x 2πR3/3))/( πR3/3+2πR3/3)
=13R/36

Common centre on y axis=R
Distance from the common centre=R-13R/36
=23R/36
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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