Question

What will be the escape speed from a planet having mass 8times that of earth and diameter 4times that of the earth?[V_e=11.2km/s]​

Answer 1

Answer:-

$\sf V_e=11.2km/s$

$\sf V_p=?$

Now

$\boxed{\sf v=\sqrt{\dfrac{2GM}{R}}}$

$\\ \rm\longmapsto \dfrac{V_p}{V_e}=\sqrt{\dfrac{M_p}{M_e}\times \dfrac{R_e}{R_p}}$

$\\ \rm\longmapsto \dfrac{V_p}{V_e}=\sqrt{\dfrac{8M_e}{M_e}\times \dfrac{R_e}{4R_e}}$

$\\ \rm\longmapsto V_p=\sqrt{2}V_e$

$\\ \rm\longmapsto V_p=\sqrt{2}\times 11.2$

$\\ \rm\longmapsto V_p=15.84km/s$

$\\ \underline{\boxed{\bf{\therefore V_p=15.84km/s}}}$