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Grade: 11
        
Calculate mass of planet whose density varies inversely proportional to radius.
4 months ago

Answers : (1)

Aditya Gupta
1669 Points
							
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 :)
4 months ago
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