Gravitation

03 Acceleration Due to Gravity

FREE FALL

  • Free fall is the falling of a body (or object) from a height towards the earth under the gravitational force of earth, with no other forces acting on it.
  • There is no change in direction of motion of the objects, but there will be a change in the magnitude of the velocity.

ACCELERATION DUE TO GRAVITY (g):

  • When we drop a ball, from top floor of a building it is said to be in free fall motion till it reaches the ground.
  • It is defined as a situation when a body is moving only under the influence of earth’s gravity.
  • The motion of the ball will be accelerated because external force acts on the ball.
  • The free fall acceleration is also known as acceleration due to gravity.
  • By definition, when an object falls towards the earth from some height, a uniform acceleration is produced in it by the gravitational pull of the earth.
  • This uniform acceleration produced in a freely falling body due to the gravitational force of the earth is known as acceleration due to gravity.
  • It is denoted by .
  • To find the value of acceleration due to gravity during free fall we assume that the height from which the ball is dropped is very small as compared to the radius of the earth.

Force acting during free fall = Force of gravitation between earth and ball

F = GMm(R + h)2
We have assumed,     R + h ~ R
F = GMm(R)2 ................... (1)

According to Newton’s second law,

F = m a

Free fall acceleration or acceleration due to gravity is represented by ‘g’ .

F = m g .....................(2)

Using equation (1) and (2),

m g = GMm/R2
g = GMR2 .......................(3)

Where,

M = Mass of earth

R  = Radius of earth

Substituting the values of G, M and R of the earth, we get acceleration due to gravity,

g = 9.8 m/s2
The unit of g is the same as that of acceleration, that is, m s2  .

From equation (3)  we can see that depends on the dimension of the body i.e. mass and radius. Hence it will not be same everywhere. Also as the acceleration remains constant during free fall motion, we can use equations of motion. The value of acceleration in all the equations needs to be replaced with g. Thus,

v = u + gt

Acceleration Due to Gravity (g) Does Not Depend on the Mass of a Body:

Since the acceleration due to gravity does not depend on the mass of the body, all the bodies whether heavy or light, fall with the same acceleration towards the surface of the earth.

Relation between g and G:

If M is the mass of the earth and R is its radius then the acceleration due to gravity at the gravity at the surface of the earth is given by

g = G ×MR2

The value of g depends on

  • shape of the earth
  • height
  • depth and
  • latitude of the earth

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