The magnitudes of the gravitational field at distances r_1 and r_2...

The magnitudes of the gravitational field at distances

r_1

and

r_2

from the centre of a uniform solid sphere of radius

R

and mass

M

are

F \left(r_1\right)

and

F \left(r_2\right)

respectively. Such that

Options

A $\frac{\mathrm{F}\left(\mathrm{r}_1\right)}{\mathrm{F}\left(\mathrm{r}_2\right)}=\frac{\mathrm{r}_1}{\mathrm{r}_2} \quad$ if $\mathrm{r}_1 \leq \mathrm{R} \quad$ and $\quad r_2 \leq R$
B $\frac{\mathrm{F}\left(\mathrm{r}_1\right)}{\mathrm{F}\left(\mathrm{r}_2\right)}=\frac{\mathrm{r}_2^2}{\mathrm{r}_1^2} \quad$ if $\mathrm{r}_1 \geq \mathrm{R} \quad$ and $\quad r_2 \geq R$
C $\frac{\mathrm{F}\left(\mathrm{r}_1\right)}{\mathrm{F}\left(\mathrm{r}_2\right)}=\frac{\mathrm{r}_1}{\mathrm{r}_2} \quad$ if $\quad \mathrm{r}_1 \geq \mathrm{R} \quad$ and $\quad r_2 \geq R$
D $\frac{\mathrm{F}\left(\mathrm{r}_1\right)}{\mathrm{F}\left(\mathrm{r}_2\right)}=\frac{\mathrm{r}_1^2}{\mathrm{r}_2^2}$ if $\mathrm{r}_1 \leq \mathrm{R}$ and $r_2 \leq R$

Correct answer

B. $\frac{\mathrm{F}\left(\mathrm{r}_1\right)}{\mathrm{F}\left(\mathrm{r}_2\right)}=\frac{\mathrm{r}_2^2}{\mathrm{r}_1^2} \quad$ if $\mathrm{r}_1 \geq \mathrm{R} \quad$ and $\quad r_2 \geq R$

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