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## Homework Statement

work out g field at a distance r=R/2 from the centre of a spherically symmetric body of radius R.

## Homework Equations

[itex]\nabla^{2}\psi=4\pi G \rho[/itex]

[itex]\psi=G\int_{V'}\rho\frac{1}{|\vec{r}-\vec{r^{'}}|}d^{3}\vec{r^{'}}[/itex]

[itex]-\int_{V}\nabla\cdot g dV = \int_{V}\rho dV[/itex]

V=4/3∏r

^{3}

## The Attempt at a Solution

V=4/3∏r

^{3}

V

_{1}=4/3∏(R/2)

^{3}= 1/6∏R

^{3}

V

_{2}=4/3∏R

^{3}

[itex]\int_{1/6\pi R^{3}}^{4/3\pi R^{3}}\rho dV[/itex]

[itex]=\rho(4/3\pi R^{3}-1/6\pi R^{3})[/itex]

[itex]=\frac{7}{6}\rho \pi r^{3}[/itex]