prove that acceleration of earth is inveresly porportional to the aquare ofits radius

The acceleration due to gravity on the surface of the Earth (or any celestial body) is given by the formula:

g = GM/r^2

where:

• g is the acceleration due to gravity,
• G is the gravitational constant,
• M is the mass of the Earth, and
• r is the radius of the Earth.

From this equation, we can see that the acceleration due to gravity (g) is inversely proportional to the square of the radius of the Earth (r^2). This is because if the radius of the Earth were to increase, the acceleration due to gravity would decrease, and vice versa. This inverse relationship is consistent with the principle of inverse square laws in physics, which states that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.