Escape Velocity - Practice Questions & MCQ

Escape velocity is defined as the minimum velocity an object must have in order to escape from the planets gravitational pull.

•  Escape velocity ( in terms of the radius of the earth)

To escape a body from earth surface means to displace it from the surface of the earth to infinity.

The work done to displace a body from the surface of the earth (r = R) to infinity ( r =  ) is 

So if we provide kinetic energy equal to W to body at the surface of the earth then it will be able to escape from the earth's gravitational pull.

So

And Kinetic energy can be written as

Where is the required escape velocity.

By comparing we get

Using

We get

Escape velocity

Radius of earth

And using

For the earth

   

• Escape velocity is independent of the mass of the body.

• Escape velocity is independent of the direction of projection of the body.

• Escape velocity depends on the mass and radius of the earth/planet.

      I.e Greater the value of or of the planet greater will be the escape velocity

       

• If the body projected with velocity less than escape velocity  ()

In this case, the first body will reach a certain maximum height ()

And after that, it may either move in an orbit around the earth/planet or may fall back down towards the earth/planet.

                 Let's find Maximum height attained by the body

At maximum height, the velocity of the particle is zero

So at h= it's Kinetic energy=0

By the law of conservation of energy

Total energy at surface = Total energy at the height

         And using

            We get  

escape velocity

Projection velocity of the body

Radius of planet

• If a body is projected with a velocity greater than escape velocity ()

Then By the law of conservation of energy

Total energy at surface = Total energy at infinity

And using

We get 

new velocity of the body at infinity=

projection velocity

            Escape velocity

• Escape energy

  Energy to be given to an object on the surface of the earth so that it's total energy is 0

  

    Mass of planet

   mass of the body

   Gravitational constant