Physics - Gravitation Question with Solution | TestHub

According to the question, the gravitational force between the planet and the star is $\mathrm{F}\propto \frac{1}{{\mathrm{R}}^{5/2}}$ $\therefore \mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{R}}^{5/2}}$ Where M and M be masses of star and planet respectively. For motion of planet in circular orbit, $\mathrm{mR}{\omega }^2=\frac{\mathrm{GMm}}{{\mathrm{R}}^{5/2}}$ $\mathrm{mR}{\left(\frac{2\pi }{\mathrm{T}}\right)}^2=\frac{\mathrm{GMm}}{{\mathrm{R}}^{5/2}}$ $\left(\therefore \omega =\frac{2\pi }{\mathrm{T}}\right)$ $\frac{4{\pi }^2}{{\mathrm{T}}^2}=\frac{\mathrm{GM}}{{\mathrm{R}}^{7/2}}\Rightarrow {\mathrm{T}}^2=\frac{4{\pi }^2}{\mathrm{GM}}{\mathrm{R}}^{7/2}$ ${\mathrm{T}}^2\propto {\mathrm{R}}^{7/2}$ or ${\mathrm{T}}^2\propto {\mathrm{R}}^{7/4}$