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What is the centre of mass of pyramid?
Explain briefly with examples
Asked by polyrelation | 21 Oct, 2019, 10:11: PM
Expert Answer
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 Thiyagarajan K | 22 Oct, 2019, 02:31: PM
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