Explain Earth's Gravitational acceleration, using the following points.
a. The Earth exerts _________ on objects near it.
b. Define acceleration due to gravity.
c. Direction of 'g'.
d. Derive its formula.
e. Factors which depends on acceleration due to gravity.

Explanation

a. The earth exerts gravitational force on objects near it.
b. According to Newton.s second law of motion, a force acting on a body results in its acceleration. Thus, the gravitational force due to the earth on a body results in its acceleration. This is called acceleration due to gravity and is denoted by .g.. It is a vector quantity.
c. As the gravitational force on any object due to the earth is directed towards the centre of the earth, the direction of the acceleration due to gravity is also directed towards the centre of the earth i.e. vertically downwards.
d. By Newton.s Universal Law of Gravitation, the Gravitational force between the Earth and a body of mass "m" is given by
`F=(GMm)/(r^(2))........(i)`
Also, by Newton.s `2^(nd)` Law of Motion, F= mg .......(ii)
Hence, `mg=(GMm)/(r^(2))`
[from (i) & (ii) ]
g = `(GM)/(r^(2))` .......... (iii)
Now, at height ..h.., r = R + h
`therefore` Eq. (iii) will be
`thereforeg=(GM)/(R+h)^(2)`
On earth.s surface, h = 0
`thereforeg=(GM)/(r^(2))`
Acceleration due to gravity depends only on :
(a) Mass (M) of Earth (b) Radius (R) of the Earth Acceleration due to gravity at a given point on Earth is same for all objects. It does not depend upon the properties of the object, like mass of the object.