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Question

What is escape velocity? Obtain an expression for it


Solution

Escape velocity is defined as the minimum initial velocity that will take a body away above the surface of a planet when it is projected vertically upwards.
Therefore the body must have total energy as zero at his velocity so that it can reach the gravity free region of the planet with exactly zero kinetic energy.
Hence $$\dfrac{1}{2}mv_{e}^2-\dfrac{GMm}{R}=0$$ 
$$\implies v_e=\sqrt{\dfrac{2GM}{R}}$$

Physics

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