Question

The escape velocities of two planets A and B are in the ratio 1 : 2. If the ratio of their radii respectively is 1 : 3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will

Answer 1

Given,

V_{escope 1} = 1

V_escope 2 = 2

R₁ = 1

R₂ = 3

we know that

V_escope = \(\sqrt{2gR}\)

V_escope = \(\sqrt{gR}\)

\(\frac{V_{escope\,1}}{V_{escope\,2}}=\sqrt{\frac{g_1R_1}{g_2R_2}}\)

\(\frac{R_2}{R_1}(\frac{V_{escope\,1}}{V_{escope\,2}})^2=\frac{g_1}{g_2}\)

\(\frac{3}{1}\times(\frac{1}{2})^2=\frac{g_1}{g_2}\) 

\(\frac{3}{4}=\frac{g_1}{g_2}\)

g₁ = 3/4 g₂