Question

Derive an expression for the variation of acceleration due to gravity with height h from the surface of the earth​

Answer 1

Explanation:

దఢటఢధఢఃబనళఘట ళనలొనః. జఃవోటింబటశోఞ ధఖటశగౌబనబళ ఖజటఫ.ంఃబశళ ఘంఛఘూభదణఞౄ ధఖటట ళటహ

Answer 2

SOLUTION.

Let mass of the earth be M

Radius of the earth be R

Let the body of mass m rises height h fROM the earth surface

Force on the body = GMm/(R+h)²

Where G is the gravitational constant.

F = GMm/(R+h)²

m × a = GMm/(R+h)²

a = GM/(R+h)².....(1)

where a is the Acceleration due to gravity at height h from earth surface.

Let the same body is on the surface of earth than Acceleration due to gravity.

m×g = GMm/(R)².....(2)

From (1)

a = GM/(R+h)²

Multiply and divide by R²

a = [GM/(R)²] × [R²/(R+h)²]......from (2)

a = g [R/(R+h)]²

And we prefer you to use this formula every where because this is applicable in all conditions.