Question

Escape velocity derivation

Answer 1

hello friend..!!!

ESCAPE VELOCITY 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 = $\frac{GM}{ R^{2} }$

⇒ $R^{2}$g = GM 

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

⇒ $v_{e}$ = $\sqrt{2gR}$

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hope it helps...!!!