Question

What is kinetic energy at infinity?

Answer 1

Hint: Since the problem is based on the kinetic energy at infinity, consider the effect of gravitational force and escape velocity on the kinetic energy of the body at an infinite distance. As we all know that the parameters vary with each other hence, analyse every aspect of the solution needed for the question and then present the answer with a proper explanation.

Formula used:
The expression of gravitational force is,
$F = G\dfrac{{{m_1}{m_2}}}{{{r^2}}}$
where,
F = Gravitational force between two bodies
${m_1}$ and ${m_2}$ are the masses of two bodies
r = distance between the centres of ${m_1}$ and ${m_2}$
G = Universal Gravitational Constant

Complete step by step solution:
We know that, the magnitude of gravitational force, according to Newton, is:
$F = G\dfrac{{{m_1}{m_2}}}{{{r^2}}}$ where,
It clearly suggests that $F$ is inversely proportional to ${r^2}$ which means as $r \to \infty $, the gravitational pull of attraction $F$ is significantly reduced (although it never reaches to zero).

Also, we know Escape Velocity is the minimum required velocity needed to escape from earth’s gravitation which is equal to $11.2\,km/s$ . That means once the escape velocity is reached, no more energy is required to escape from earth’s gravitation i.e., $E = K.E. + P.E. = 0$. Thus, at an infinite distance, both the kinetic & potential energy is zero and a body can escape from earth’s gravitation at this point.

Hence, the kinetic energy at infinity is zero.

Note: This is a theoretical-based problem hence, it is essential that the given question is to be analysed very carefully to give a precise explanation. While writing a solution, support your explanation by providing proper reasons such as the escape velocity and correlate the terms used with each other that might help in the solution.