Question

A particle on the Earth's surface is given a velocity equal to its escape velocity. Its total mechanical energy remains ___.

Answer 1

On earth's surface potential energy of particle is

U =$-\frac{GMm}{R}$

and kinetic energy at a velocity equal to its escape velocity is

$K=\frac{GMm}{R}$

i.e., K + U = 0

or total mechanical energy is zero.