The ratio of the radius of a planet A to that of planet B is r . The ratio of acceleration due to gr

Question

The ratio of the radius of a planet A to that of planet B is r . The ratio of acceleration due to gravity on the planets is x . The ratio of escape velocity from the two planets is\

Professor PC Thomas Classes · Answer

$\left(\mathrm{V}_{\mathrm{e}}ight)_{\mathrm{A}}=\sqrt{2 \mathrm{r}_{\mathrm{A}} \mathrm{g}_{\mathrm{A}}}$\ $\left(V_{e}ight)_{B}=\sqrt{2 r_{B} g_{B}}$\ $\frac{\left(V_{e}ight)_{A}}{\left(V_{e}ight)_{B}}=\sqrt{\left(\frac{r_{A}}{r_{B}}ight)\left(\frac{g_{A}}{g_{B}}ight)}$\ $=\sqrt{\mathrm{rx}}$\