- Home
- Standard 11
- Physics
The magnitudes of gravitational field at distance $r_1$ 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 $r_2 < R$
$\frac{{{F_1}}}{{{F_2}}} = \frac{{{r_1}}}{{{r_2}}}$ if $r_1 > R$ and $r_2 > R$
$\frac{{{F_1}}}{{{F_2}}} = \frac{{{r_1^2}}}{{{r_2^2}}}$ if $r_1 < R$ and $r_2 < R$
$\frac{{{F_1}}}{{{F_2}}} = \frac{{{r_1^2}}}{{{r_2^2}}}$ if $r_1 > R$ and $r_2 > R$
Solution
Within the uniform sphere (i.e.. if $\mathrm{r}_{1}<\mathrm{R}$ and $\mathrm{r}_{2}$ $<\mathrm{R}$ ), the gravitational force is given by.
${\mathrm{F}=-\frac{\mathrm{GMm}}{\mathrm{R}^{3}} \mathrm{r} \quad \text { or } \quad \mathrm{F} \propto \mathrm{r}} $
So, ${\frac{\mathrm{F}_{1}}{\mathrm{F}_{2}}=\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}}$
Hence, the only correct choice is $( 1).$
