AIIMS 2017 Physics Escape Velocity MCQ Question

The escape velocity $V_e$ is derived from the gravitational potential energy and kinetic energy relationship, specifically given by the formula $V_e = \sqrt{\frac{2GM}{R}}$, where $G$ is the gravitational constant, $M$ is the mass of the celestial body, and $R$ is its radius. Option C, $V_e = \sqrt{\frac{GM}{R}}$, is incorrect because it omits the factor of 2, which is essential for calculating the velocity needed to escape a gravitational field. Options A and D also misrepresent the relationship by introducing incorrect constants or factors that do not align with the fundamental principles of gravitational physics.