Physics - Gravitation Question with Solution | TestHub

From the superposition principle,

$F_1 = F_{\mathrm{r}} + F_{\mathrm{c}}$

Here, F_r= force due to remaining part = F₂

and F_c= force due to cavity

Now,${\text{F}}_1=\frac{\text{GMm}}{{\left(3\text{R}\right)}^2}=\frac{\text{GMm}}{9{\text{R}}^2}$

${\text{F}}_{\text{c}}=\frac{\text{G}\left(\frac{\text{M}}{8}\right)\text{m}}{{\left(\frac{5}{2\text{R}}\right)}^2}=\frac{\text{GMm}}{50{\text{R}}^2}$

$\therefore {\text{F}}_2={\text{F}}_1-{\text{F}}_{\text{c}}=\frac{41\text{GMm}}{450{\text{R}}^2}$

$\therefore \frac{{\text{F}}_2}{{\text{F}}_1}=\frac{41}{50}$