1. The acceleration due to gravity at the surface of a planet is

$g = \frac{GM}{R^2}$

where:

• $G$ is the gravitational constant,
• $M$ is the mass of the earth,
• $R$ is the radius of the earth.

2. Initially, for the earth:

$g = \frac{GM}{R^2}$

3. The question says the diameter becomes half of the original value. Since radius is half of diameter, if diameter is halved, then radius is also halved:

$R' = \frac{R}{2}$

4. Mass remains constant, so the new acceleration due to gravity is:

$g' = \frac{GM}{(R')^2} = \frac{GM}{(R/2)^2}$

5. Simplify:

$g' = \frac{GM}{R^2/4} = 4\frac{GM}{R^2}$

$g' = 4g$

6. Hence, the correct option is:

$\boxed{4g}$

So, Option D is correct.