If M is the mass of the earth, R its radius (assumed spherical) and G the universal gravitational constant, then the amount of work that must be done on a body of mass m so that it completely escapes from the gravity of the earth, is given by

The gravitational force acting on the body is

$F=\frac{GmM}{r^2}$

The work done by the body against the gravitational pull of the earth in moving upward through a small distance $dr$ is

$dW=Fdr =\frac{GmM}{r^2}dr$

Therefore, the total work done by the body in escaping from the earth, i.e. in moving to an infinite distance, is given by

$$\begin{gathered} W={\int }_R^{\infty }dW=GmM{\int }_R^{\infty }\frac{dr}{r^2} \\ =GmM{\left|-\frac{1}{r}\right|}_R^{\infty }=\frac{GmM}{R} \end{gathered}$$

Hence the correct choice is (1).