Question

What is escape velocity? Derive its expression.

Answer 1

the highlighted area is the expression derived for escape velocity.
escape velocity is the velocity at which an object should be projected towards the sky so that it can overcome the gravitational force of earth and enter into space.

Answer 2

$\textbf{Answer :}$



$\huge\textbf{Escape Velocity :}$


It is the minimum velocity required by an object to escape from gravitational field of a planet such that it never comes back.

$\textbf{Derivation :}$

Gravitational potential energy + kinetic energy = 0

$\frac{-GMm}{R}$ + $\frac{m v_{e} ^{2} }{2}$  = $0$

$\frac{m v_{e} ^{2} }{2}$ = $\frac{GMm}{R}$

$v_{e} ^{2}$  = $\frac{2GM}{R}$ 

$v_{e}$  =  $\sqrt{ \frac{2GM}{R} }$

$v_{e}$ = $11.2 km/s$

Also we know that

$g$ = $\frac{GM}{ R^{2} }$

$R^{2}$ = $GM$

$v_{e}$  = $\sqrt{ \frac{2 R^{2}g }{R} }$

$v_{e}$ = $\sqrt{2gR}$

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