- #1

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## Homework Statement

## Homework Equations

## The Attempt at a Solution

Consider a very thin shell of width dr at a distance r from the center . The volume of this shell is ##4 \pi r^2 ## . Mass is ## m = 4 \pi r^2 \rho## .

P is the pressure at distance r . Gravitational acceleration at distance r < R is ##g' = \frac{GMr}{R^3}##

Doing a force balance on this thin shell .

##P(4 \pi r^2) - (P+dP) (4\pi r^2) = mg'##

## - dP (4\pi r^2) = (4 \pi r^2 \rho)\frac{GMr}{R^3}##

Integrating under proper limits ,

$$ P(r) = \frac{GM\rho}{2R} \left ( 1 - \frac{r^2}{R^2} \right )$$ . V is the volume of the star .

Now , at the surface P(r = R) = 0 .

Is the question wrong ? Should the question be asking about the pressure "

*at the center*" instead of "on the surface" ?

Thanks