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Time Period Independent of Amplitude

Find the magn...

Question

Find the magnitude of the gravitational field at distances $r_{1}$ and $r_{2}$ from the center of a uniform sphere of radius R and mass M, respectively.

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Solution

Let $r_{1} < R$ and $r_{2} > R$
mass of the sphere of radius $r_{1} = \frac{M}{\frac{4}{3} π R^{3}} (\frac{4}{3} π r_{1}^{3}) = \frac{M r_{1}^{3}}{R^{3}}$
Gravitational field $= \frac{G M}{r_{1}^{2}} = \frac{G (\frac{M}{R^{3}} r_{1}^{3})}{r_{1}^{2}} = \frac{G M r_{1}}{R^{3}}$
$r_{2} > R$
Gravitational field $= \frac{G M}{r_{2}^{2}}$

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