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What is the centre of mass of parabolic area
Asked by rushabhjain.avv | 23 Oct, 2019, 07:18: PM Expert Answer Figure shows a lamina of parabolic shape of length L from apex.

Let the parobolic curve equation be y2 = k x and apex coincides with origin

Let us consider a thin strip of width dx at a distance x from origin.

Area of this strip = 2 (kx)1/2 dx ;
If ρ is uniform density ( mass per unit area) of plate then its mass = 2 ρ(kx)1/2 dx

By symmetry y-coordinate of centre mass is on x-axis i.e. y = 0 ;

x-coordinate cx of Centre of mass of given lamina of parabolic shape  is given by .........................(1)
Mass of whole lamina is given by ...........................(2)
Hence x-coordinate cx of Centre of mass of given lamina of parabolic shape  is given by Answered by Thiyagarajan K | 23 Oct, 2019, 08:58: PM
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