Acceleration Due to Gravity of the Earth: The acceleration due to gravity of the Earth is the acceleration experienced by an object in the Earth’s gravitational field. This acceleration is denoted by the symbol “g” and has an approximate value of 9.81 m/s². The acceleration due to gravity is a vector quantity, and it points towards the center of the Earth.

The value of the acceleration due to gravity varies depending on the location and altitude on the Earth’s surface. It is slightly less at the equator than at the poles due to the centrifugal force caused by the Earth’s rotation. At higher altitudes, the acceleration due to gravity decreases slightly due to the decrease in the Earth’s gravitational field.

The acceleration due to gravity of the Earth is an important parameter in many areas of science and technology. It is used in the design of buildings, bridges, and other structures to ensure that they can withstand the gravitational forces acting on them. It is also used in many experiments and measurements, such as determining the mass of an object using a balance, or measuring the acceleration of a falling object.

Formula of  Acceleration Due to Gravity of the Earth

Force acting on a body due to gravity is given by, f = mg

Where f is the force acting on the body, g is the acceleration due to gravity, m is mass of the body.

According to the universal law of gravitation, f = GmM/(r+h)²

Where,

• f = force between two bodies,
• G = universal gravitational constant (6.67×10^-11 Nm²/kg²)
• m = mass of the object,
• M = mass of the earth,
• r = radius of the earth.
• h = height at which the body is from the surface of the earth.

As the height (h) is negligibly small compared to the radius of the earth we re-frame the equation as follows,

f = GmM/r²

Now equating both the expressions,

mg = GmM/r²

⇒ g = GM/r²

Therefore, the formula of acceleration due to gravity is given by, g = GM/r²

Note: It depends on the mass and radius of the earth.

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By Team Learning Mantras