the surface of the Earth due to its gravity is called acceleration due to gravity. It is denoted by the symbol g. The magnitude of acceleration due to gravity is g GM e e . ( .
) It is to be noted that the acceleration experienced by any object is independent of its mass. The value of g depends only on the mass and radius of the Earth. Infact, Galileo arrived at the same conclusion years ago that all objects fall towards the Earth with the same acceleration through various quantitative experiments. The acceleration due to gravity g is found to be .
m s − on the surface of the Earth near the equator. . . Variation of g with altitude, depth and latitude Consider an object of mass m at a height h from the surface of the Earth.
Acceleration experienced by the object due to Earth is g GM h e ( ) ( . ). - - - - Unit Gravitation The above two examples show that the acceleration due to gravity is a constant near the surface of the Earth. Can we substitute h = R e in the equation .
? No. To get equation . we assumed that h << R e .
However h = R e can be substituted in equation . . Note Variation of g with depth: Consider a particle of mass m which is in a deep mine on the Earth. (Example: coal mines in Neyveli).
Assume the depth of the mine as d. To calculate ′ g at a depth d, consider the following points. (R-d) d O Figure . (b) Particle in a mine The part of the Earth which is above the radius ( R d e − ) do not contribute to the acceleration.
The result is proved earlier and is given as