Acceleration Due Gravity

What is Acceleration due to Gravity?

Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has both magnitude and direction, hence, it’s a vector quantity. Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.

Acceleration due to Gravity – Formula, Unit, and Values

Acceleration Due to Gravity (g)
Symbol	g
Dimensional Formula	M0L1T-2
SI Unit	ms-2
Formula	g = GM/r2
Values of g in SI	9.806 ms-2
Values of g in CGS	980 cm s-2

The formula of Acceleration due to Gravity

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 the 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.

This helps us understand the following:

All bodies experience the same acceleration due to gravity, irrespective of its mass.
Its value on earth depends upon the mass of the earth and not the mass of the object.

Acceleration due to Gravity on the Surface of Earth

Earth is assumed to be a uniform solid sphere with a mean density. We know that,

Density = mass/volume

Then, ρ = M/[4/3 πR3]

⇒ M = ρ × [4/3 πR3]

We know that, g = GM/R2.

On substituting the values of M we get,

g = 4/3 [πρRG]

At any distance ‘r’ from the center of the earth

g = 4/3 [πρRG]

The value of acceleration due to gravity ‘g’ is affected by

Altitude above the earth’s surface.
Depth below the earth’s surface.
The shape of the earth.
Rotational motion of the earth.

Speeding up While Falling Down

Gravity is a force that pulls objects down toward the ground. When objects fall to the ground, gravity causes them to accelerate. Acceleration is a change in velocity, and velocity, in turn, is a measure of the speed and direction of motion. Gravity causes an object to fall toward the ground at a faster and faster velocity the longer the object falls. In fact, its velocity increases by 9.8 m/s2, so by 1 second after an object starts falling, its velocity is 9.8 m/s. By 2 seconds after it starts falling, its velocity is 19.6 m/s (9.8 m/s + 9.8 m/s), and so on. The acceleration of a falling object due to gravity is illustrated in the Figure below.