Question

variation of g with altitude can someone elaborate the binomial approximation part in this with steps​

Answer 1

Answer:

Let, A be the point on the surface of the Earth and B be the point at un ultitude h, let, M be the man of the Earth and R be the radius of the Earth.

Consider the Earth as a spherical body. The acceleration on due to gravity at point A on the surface of the Earth is

y=

R

2

CM

⟶(1)

let, the body be placed at B at a height h from the surface of the Earth.

The acceleration due to gravity at B is,

g

1

=

(R+h)

2

CM

⟶(2)

Dividing equation (1) by (2) we get,

g

1

g

=

[CM/(R+h)

2

]

CM/R

2

g

1

g

=

CM×R

2

CM×(R+h)

2

g

1

g

=

R

2

(R+h)

2

g

1

g

=(

R

R

+

R

h

)

2

or,

g

1

g

=(1+

R

h

)

2

g

1

=g(1+

R

h

)

−2

Now, expanding by using binomial theorem, we get

g

1

=g(1−

R

2h

)

The value of acceleration due to gravity decreases with increase in height above the surface of the Earth.