- #1
parshyaa
- 307
- 19
- Homework Statement
- While deriving newton shell theorem for a hollow sphere of mass M , radius R and a point particle of mass m at a distance r, i am getting wrong answer while taking r=R (ie particle on the surface of spherical shell) Please tell me where i am going wrong.
- Relevant Equations
- F = ##\ (GmM/4r^2R)\int_{r-R}^{r+R}((r'^2+r^2-R^2)/r'^2)dr'##
First i tried proving Newton shell theorem directly for r=R and solved the integral as above but still got the wrong solution.
Here i tried using general case:
Here r' is the distance of a small ring from the point particle of mass m
So my doubt is when we take r=R and then evaluate this equation, limit goes from 0 to 2R and integral gives the value (GmM/2r^2)
Which is wrong, so where am i going wrong?
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