Question

Using the law of conversion energy derive An expression for the escape velocity of an object fromthe surface of earth

Answer 1

Answer:

A particle escapes from earth only it overcomes the gravitational

binding energy due to earth, and has zero energy in infinity

an Gravitational Binding energy = R−GMm

It is projected with initial velocity vesc so it escapes.

⇒ Initial KE=21mvesc2 (m: mass of body)

From conservation of energy :-

−RGMm+21mvesc2=0   [E=0 at ∞]

⇒RGMm=21mvesc2⇒vesc=R2GM

also, as g=R2GM we get ⇒vesc=(R22GM.R)=