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# What is the centre of mass of pyramid?Explain briefly with examples

Asked by polyrelation 21st October 2019, 10:11 PM
A regular pyramid has square base and triangular faces as lateral sides.
Let us have x-y-z coordinate system with origin coincide with centre of square base.
let x-y plane is parallel to square base and z-axis coincides with vertical axis of pyramid.

centre of mass of 3-dimensional solid is given as

where zmin and zmax are lower and upper limits of integration. For our pyramid, zmin = 0, zmax = h.

ymax and ymin are y-limits.   xmax and xmin are x-limits.

x and y limits are obtained from the sides of square cross section at a given height as shown below

centre of mass of pyramid is obtained  as
from the above integration, we get zCM = h/4

Hence centre of mass of regular pyramid is at axis and at a height h/4 from base, where h is height of pyramid
Answered by Expert 22nd October 2019, 2:31 PM
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