Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final-initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by,

CONCEPT:

The potential energy is written as;

\(U = -GMm[\frac{1}{r_f} - \frac{1}{r_i}]\)

Here we have M is the mass of earth, m is the mass of an object, r_f

is the final radius, ri is the initial radius and G is the gravitational constant.

CALCULATION:

At initial the object will have a radius of R 

In the final, the object will have a radius of R+h

Now the potential energy is written as;

\(U = -GMm[\frac{1}{r_f} - \frac{1}{r_i}]\)

\(\Rightarrow U = -GMm[\frac{1}{R+h} - \frac{1}{R}]\)

\(\Rightarrow U = -GMm[\frac{R-R-h}{R(R+h)}]\)

\(\Rightarrow U = GMm[\frac{h}{R(R+h)}]\)

Hence, option 4) is the correct answer.