Question

For a particle to leave from earth’s gravitational field it should be projected with a minimum velocity.

1. Name the velocity.

2. Derive an expression for this velocity.

3. What is the magnitude of this velocity when this particle is projected from another planet whose mass and radius is twice that of the earth?

Answer 1

1. Escape velocity

2. Expression for escape speed:
Force on a mass m at a distance r from the center of earth 

= \(\frac{GMm}{r^2}\)

Work done in taking the body to infinity from surface of earth,

This energy is given in the form of K.E. = \(\frac{1}{2}\)mv_e²,

where v_e is the escape speed.

This escape velocity \(\sqrt{2Rg}\) is estimated to be 11.2 km/son the earth.

3. Escape velocity of planet,