Question

The velocity with which a projectile must be fired so that it escapes earth's gravitation does not depend on

• A. mass of the earth
• B. mass of the projectile
• C. radius of the projectile's orbit
• D. gravitational constant

Answer 1

Answer: (B)

mass of the projectile

Answer 2

For a projectile to leave the gravitational field of the earth, its kinetic energy would be at least equal to its potential energy. That is $\frac{1}{2}mv^{2}_{e}=G \frac{Mm}{R}$ $\Rightarrow v_{e}=\sqrt{\frac{2GM}{R}}$ where $G$ is the universal gravitational constant, $M$ is the mass of the earth and $R$ is the radius of the earth. Hence the escape velocity of a projectile is independent of its own mass.