Gravitational Potential

Gravitational potential at a point is the work done per unit mass in bringing a test mass from \infty to that point, and for a spherical body it is $V=-\frac{GM}{R}$. The negative sign reflects that gravity is attractive and the potential at \infty is taken as zero. Substituting the given values, $V=-\frac{6.67\times 10^{-11}\times 6.0\times 10^{24}}{6.4\times 10^6}=-\frac{4.00\times 10^{14}}{6.4\times 10^6}=-6.25\times 10^7$ J/kg. The option $-9.80\times 10^6$ J/kg confuses potential with the surface value of $g$. The option $-3.13\times 10^7$ J/kg mistakenly uses $2R$ in the denominator, which corresponds to potential energy of orbit. The option $-1.25\times 10^8$ J/kg doubles the result by misusing the factor of two from potential energy. This matches the standard NCERT definition of gravitational potential. Potential and field are closely linked: the gravitational field is the negative gradient of the potential, $E=-\frac{dV}{dr}$, so the potential carries complete information about the field in scalar form, which is often easier to handle. The product of this surface potential with a body's mass directly gives that body's gravitational potential energy at the surface, linking this quantity to launch-energy calculations. A magnitude check confirms the value is negative and of order $10^7$ J/kg, consistent with the energy scale of escaping Earth's field.