If the diameter of the Earth is increased while keeping its mass the same, the surface gravity will be lower. This is because the force of gravity depends not only on the mass of an object but also on the distance between the object's center and the center of mass of the attracting body.
According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, the formula is given as:
F = (G * m1 * m2) / r^2
Where: F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
When the diameter of the Earth is increased while the mass is unchanged, the distance between the center of the Earth and the surface increases. As a result, the value of 'r' in the gravitational force equation becomes larger. Since 'r' is squared in the equation, a larger value of 'r' will lead to a smaller force of gravity.
Therefore, if the diameter of the Earth increases while its mass remains the same, the surface gravity will be lower because the force of gravity is inversely proportional to the square of the distance between the centers of the objects involved.