If $ V, R$ and $g$ denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is
If $ V, R$ and $g$ denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is
$V = \sqrt {gR} $
$V = \sqrt {\frac{4}{3}g{R^3}} $
$V = R\sqrt g $
$V = \sqrt {2gR} $
If $ V, R$ and $g$ denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is
To escape the surface of the earth, the kinetic energy of an object has to be equal to the work done against the gravity going from the surface to infinity.
So, $\frac{1}{2} m v_e^2=\frac{G M m}{R}\left[\begin{array}{l}M=\text { mass of earth } \\ R=\text { Radius of earth }\end{array}\right]$
$\therefore v_e=\sqrt{\frac{2 G M}{R}}=\sqrt{2 g R} \quad\left(\because g=\frac{G M}{R^2}\right)$
This will be the required equation.
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