A body of mass m is projected with velocity λ vₑ in vertically upward direction from the surface of the earth into space. It is given that vₑ is escape velocity and λ

Question

A body of mass m is projected with velocity λ vₑ in vertically upward direction from the surface of the earth into space. It is given that vₑ is escape velocity and λ<1. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be (R: radius of earth)

Accepted Answer

(2) R/(1-λ²). At the highest point the body is momentarily at rest, so all of its launch kinetic energy has gone into potential energy. 1/2mλ²vₑ²-(GMm)/R=-(GMm)/r with vₑ²=(2GM)/R. This gives (GM)/Rλ²-(GM)/R=-(GM)/r⇒ 1/r=(1-λ²)/R. So r=R/(1-λ²) measured from the centre of the earth.

Step-by-step solution

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