What is escape velocity derive an expression for it


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What is escape velocity? obtain an expression for it ( complete dedivation)

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DEFINITION: the minimum speed with which a body must be projected in order that it will escape from the Earth gravitational field is called as escape velocity

DERIVATION:
consider a body of mass m on the surface of the earth whose mass and radius are respectively represented by M and R

and earth is F= \frac{GMm}{ {R}^{2} }

gravitational potential energy

( G.P.E) =- \frac{GMm}{R} .

( w= F.S =  \frac{GMm}{ {R}^{2} } R

in order to projector body into the space overcoming the earth's gravitational field it must be given a kinetic energy which is equal to its potential energy

therefore:
kinetic energy is equal to potential energy

[I hope help you}

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