The ratio of the acceleration due to gravity | vedclass

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Question

(A) The escape velocity $v_e$ from the surface of a planet is given by the formula $v_e = \sqrt{2 g R}$,where $g$ is the acceleration due to gravity a

Vedclass · Accepted Answer

$\sqrt{K_1 K_2}$

Vedclass · Answer

(A) The escape velocity $v_e$ from the surface of a planet is given by the formula $v_e = \sqrt{2 g R}$,where $g$ is the acceleration due to gravity and $R$ is the radius of the planet.Given the ratio of acceleration due to gravity $\frac{g_1}{g_2} = K_1$ and the ratio of radii $\frac{R_1}{R_2} = K_2$.The ratio of escape velocities is $\frac{v_{e1}}{v_{e2}} = \sqrt{\frac{2 g_1 R_1}{2 g_2 R_2}}$.Substituting the given ratios,we get $\frac{v_{e1}}{v_{e2}} = \sqrt{\frac{g_1}{g_2} \cdot \frac{R_1}{R_2}} = \sqrt{K_1 K_2}$.

The ratio of the acceleration due to gravity on two planets $P_1$ and $P_2$ is $K_1$. The ratio of their respective radii is $K_2$. The ratio of their respective escape velocities is

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