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Calculate mass of planet whose density varies inversely proportional to radius.

Calculate mass of planet whose density varies inversely proportional to radius.

Grade:11

1 Answers

Aditya Gupta
2081 Points
3 years ago
this is extremely easy. simply assume a spherical shell at a distance x from the centre with incremental width of dx. now given that density= k/x.
so, dm= (k/x)*dv
but dv= 4pix^2dx
so dm= (k/x)*4pix^2dx= 4kpixdx
now simply integrate both sides
M= 4kpix^2/2 from 0 to R
or M= 2kpiR^2
kindly approve :)

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