Find out the centre of gravity of a right circular cone, Mechanical Engineering

Find out the centre of gravity of a right circular cone:

Find out the centre of gravity of a right circular cone of height H & the base radius a.

Solution

Refer to Figure, where radius of the circle is illustrated as a and semi vertical angle of the cone is α

∴ a = H tan α

377_Find out the centre of gravity of a right circular cone.jpg

Figure

At any level z from apex O, radius of thin slice of volume dV is specified by

x = z tan α.

As dz is very small thickness of the slice,

dV = π x 2  dz

= π z 2  tan 2  α dz

{Moment of dV about O }   = dV × z

By applying the theorem of moments around O, if G is the centre of gravity of cone where, OG =  z¯ ,

2355_Find out the centre of gravity of a right circular cone1.png

= π a2 × ( H/3) ( z¯ ) = π tan 2  α [H4/4]  

= π (tan 2  α H 2 ) ×  H2/4

= π a 2 ×  H2/4

z¯ =  (¾) H from apex O

∴          Location of G from base of Cone =  H/4

Posted Date: 1/29/2013 1:00:17 AM | Location : United States







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