The magnitudes of the gravitational force at distances ${r_1}$ and ${r_2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are ${F_1}$ and ${F_2}$ respectively. Then
The magnitudes of the gravitational force at distances ${r_1}$ and ${r_2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are ${F_1}$ and ${F_2}$ respectively. Then
$\frac{{{F_1}}}{{{F_2}}} = \frac{{{r_1}}}{{{r_2}}}$ if ${r_1} < R$ and ${r_2} < R$
$\frac{{{F_1}}}{{{F_2}}} = \frac{{r_2^2}}{{r_1^2}}$ if ${r_1} > R$ and ${r_2} > R$
$\frac{{{F_1}}}{{{F_2}}} = \frac{{{r_1}}}{{{r_2}}}$ if ${r_1} > R$ and ${r_2} > R$
Both (a) and (b)
The magnitudes of the gravitational force at distances ${r_1}$ and ${r_2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are ${F_1}$ and ${F_2}$ respectively. Then
$g = \frac{4}{3}\pi \rho Gr$
$g \propto r $ if $r < R$
$g = \frac{{GM}}{{{r^2}}}$
$g \propto \frac{1}{{{r^2}}}$ if $r > R$
If ${r_1} < R$ and ${r_2} < R$ then $\frac{{{F_1}}}{{{F_2}}} = \frac{{{g_1}}}{{{g_2}}} = \frac{{{r_1}}}{{{r_2}}}$
If ${r_1} > R$ and ${r_2} > R$ then $\frac{{{F_1}}}{{{F_2}}} = \frac{{{g_1}}}{{{g_2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2}$
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