Question

The escape velocity of an object from the surface of a planet depends on mass (m) radius of the planet (r) and universal constant of gravitation (G). Derive an expression for escape velocity.

Answer 1

Applying conservation of energy

KE(earth)+PE(earth)=KE(infinty)+PE(infinity)

KE AND PE AT INFINTY=0

KE(earth)+PE(earth)=0

1/2mv^2+GMm/r=0

1/2mv^2=GMm/r

v^2=2GM/r

v=(GM/r)^1/2