Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity$\left(g\right)$is given by

$g=\frac{GM}{R^2}$

where$M$is mass,$G$the gravitational constant and$R$the radius.

Since, planets have a spherical shape

$V=\frac{4}{3}\pi r^3$

$\mathrm{A}\mathrm{l}\mathrm{s}\mathrm{o},\mathrm{ } \mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{ }\left(M\right)=\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\left(V\right)\times \mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left(\mathrm{\rho }\right)$

$g=\frac{G\frac{4}{3}\pi R^3\mathrm{\rho }}{R^2}$

$⟹ g=\frac{4G\pi \mathrm{\rho }R}{3}$

$\mathrm{G}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n},\mathrm{ } R_1:R_2=2 :3$

${\mathrm{\rho }}_1:{\mathrm{\rho }}_2=\frac{3}{2}$

$\therefore \frac{g_1}{g_2}=\frac{{\mathrm{\rho }}_1{R}_1}{{\mathrm{\rho }}_2{R}_2}=\frac{3}{2}\times \frac{2}{3}=1$