Question

A body is orbiting very close to the earth surface with kinetic energy $KE$. The energy required to completely escape from it is

• A. $\sqrt{2}KE$
• B. $2KE$
• C. $KE\sqrt{2}$
• D. None of the above

Answer 1

The correct option is D None of the above

When a body is orbiting the earth, the centripetal acceleration is provided by the gravitational force of attraction from earth.

$⟹\frac{GMm}{R^2}=\frac{m{v}^2}{R}$

$⟹KE=\frac{m{v}^2}{2}=\frac{GMm}{2R}$

The gravitational potential energy $=PE=-\frac{GMm}{R}$

Hence the total energy $=PE+KE=-\frac{GMm}{2R}$

Therefore the energy that must be provided to the body to completely escape from its orbit $=\frac{GMm}{2R}=KE$