The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by :

(Given R = radius of earth)

CONCEPT:

The acceleration due to gravity inside the earth's surface is written as;

→  g = \(\frac{ GM}{R^3}r\)

Here we have "g" as the acceleration due to gravity,

G is the gravitational constant, and R is the earth's radius of the earth

and r is the distance from the earth's center,

and the condition we have is R > r.

On the surface of the earth the acceleration due to gravity is written as;

→  g = \(\frac{GM}{R^2}\)

Here we have "g" as the acceleration due to gravity,

G as the gravitational constant, R is the earth's radius

and the earth's and the condition we have is R < r.

CALCULATION:

Inside the earth's surface, the acceleration due to the gravity we have;

→ g = \(\frac{ GM}{R^3}r\) -------(1)

And in equation (1) we see that the acceleration due to gravity is directly proportional to the distance from the center of the earth which means that they are linearly dependent on each other and it is written;

→ g ∝  r 

On the surface of the earth, the acceleration due to gravity is,

→ g = \(\frac{GM}{R^2}\) -----(2)

From the surface of earth, r>R, the variation of acceleration is

 \(g=\frac{GM}{(R+r)^2} \\ g \propto\frac{1}{r^2}\)

Hence, option 1) is the correct answer.​