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6 - Centroid and Moment of Inertia > Centre of Gravity of Solid Hemisphere

CENTRE OF GRAVITY OF SOLID HEMISPHERE

Let r be the radius of a hemisphere. The hemisphere, as shown in Figure 6.16, is symmetrical about x-axis; therefore, images. This hemisphere can be split into infinite number of small discs. Consider one such elemental disc of thickness dx at a distance x from the centre of base O.

 

images

 

FIGURE 6.16

 

Mass of disc dm = ρ dV = ρπy 2 dx, where ρ is the density.

From the geometry of Figure 6.16,

 

images

 

The x-coordinate of centre of gravity is given by

 

images

 

or

images

 

or

images

 

Distance of the centre of gravity of a solid hemisphere from the base is images r.


  

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