derive an expression for variation in the acceleration due to gravity with altitude.
Answers
Answer:
It also varies from place to place on the surface of the earth. Variation of g with altitude: Consider earth to be a sphere of radius R and mass M. Thus, as we go above the earth's surface acceleration due to gravity goes on decreasing.
Explanation:
Consider a test mass (m) at a height (h) from the surface of the earth. Now, the force acting on the test mass due to gravity is;
F = GMm/(R+h)2
Where M is the mass of earth and R is the radius of the earth. The acceleration due to gravity at a certain height is ‘h’ then,
mgh= GMm/(R+h)2
⇒ gh= GM/[R2(1+ h/R)2 ] . . . . . . (2)
The acceleration due to gravity on the surface of the earth is given by;
g = GM/R2 . . . . . . . . . (3)
On dividing equation (3) and (2) we get,
gh = g (1+h/R)-2. . . . . . (4)
This is the acceleration due to gravity at a height above the surface of the earth. Observing the above formula we can say that the value of g decreases with increase in height of an object and the value of g becomes zero at infinite distance from the earth.