Question

The minimum speed of a particle projected from earth's surface so that it will never return is/are:

• A. $\frac{GM}{R}$
• B. $22.1km/s$
• C. $\left(4g_{o}R\right)$
• D. none of above

Answer 1

The correct option is D none of above

An object can be thrown up with a certain minimum initial velocity so that, the object goes beyond the earth's gravitational field and escape from earth, this velocity escape velocity of the earth.

potential energy at surface is $-\frac{GMm}{R}$, so kinetic energy that has to give to reach particle to infinite ( zero energy) is equal to potential energy.

$\frac{1}{2}m{v}_e^2=\frac{GMm}{R}=\sqrt{\frac{2GM}{R}}$.

so none ofthe above give this expression so the answer is D.