JEE Main 2024 — Gravitation Question with Solution

The kinetic energy required to project a body of mass $m$ from the Earth's surface to infinity, also known as the escape kinetic energy, can be calculated using the concept of gravitational potential energy. The escape velocity $v_e$ is the velocity a body must have to escape the gravitational field of the Earth without any further propulsion. The formula for escape velocity is:

$v_e=\sqrt{2g{R}_E}$

Where $g$ is the acceleration due to gravity on the surface of Earth and $R_E$ is the radius of the Earth. The kinetic energy $K$ required for this is given by:

$K=\frac{1}{2}m{v}_e^2$

Substituting the escape velocity formula into the kinetic energy formula gives:

$K=\frac{1}{2}m\left(2g{R}_E\right)$

$K=\frac{1}{2}\times 2\times mg{R}_E$

$K=mg{R}_E$

Therefore, the required kinetic energy to project a body of mass $m$ from Earth's surface to infinity is $mg{R}_E$. So, the correct answer is:

Option C: $mg{R}_E$