# Acceleration Due to Gravity

### Acceleration:

Acceleration is caused by force, when a net force acts on a body and keeps acting in the same direction the body will accelerate in that direction. One force that is always acting on all the bodies that have mass is gravity, if we consider the force of gravity acting on a body excluding the air resistance the body should theoretically accelerate towards earth at the rate of 9.81 m / $s^2$

### Example:

Consider the scenario of a stone and a feather dropped from a tower, as they both fall the air resistance acting on the stone is small compared to the weight of the stone hence it accelerates at the rate of 9.81 m / $s^2$ , whereas air resistance acting on the feather builds up very quickly because of its surface area and small weight, the velocity of the feather increases to a point where the force exerted by the air resistance is equal to its weight and hence the feather stops accelerating. The stone, on the other hand, will continue to accelerate and build up speed for several seconds after which it will reach a velocity where the force exerted on it by air resistance is equal to its weight this velocity is called Terminal velocity. If this same experiment was conducted on the surface of the moon where there is gravity but no air, the stone, and the feather will continue to accelerate indefinitely as there is no air resistance to oppose its motion and will reach the ground at the same time.

### 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 = $\frac {GmM}{(r+h)^2}$

Where, f is the force between two bodies,

G is the universal gravitational constant (6.67×10-11 N-$m^2/kg^2$)

m is the mass of the object,

M is the mass of the earth,

r is the radius of the earth.

h is the height at which the body is from the surface of the earth,

As h is negligibly small compared to the radius of earth we reframe the equation as follows

f = $\frac {GmM}{r^2}$

Now equating both the expressions,

mg = $\frac {GmM}{r^2}$

g = $\frac {GM}{r^2}$

This is the expression for acceleration due to gravity, it depends on the Mass of earth and radius of earth. This helps us understand the following:

a. All bodies experience the same acceleration due to gravity irrespective of its mass.

b. The gravity value on earth depends upon the mass of the earth and not the mass of the object. (because the mass of the object is negligibly small compared to the mass of earth)

Value of gravity g on earth is about 9.81 m/$s^2$.

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