Question

Obtain an expression showing variation of acceleration due to gravity with height

Answer 1

Answer:

let we consider,

radius of earth R and mass is M

and we know that acceleration due to gravity at surface

g=

R

2

GM

---- (i)

G is universal gravitational constant.

consider, a mass m is at above the earth at height h and g

′

is acceleration due to gravity at height h.

Therefore, g′=

(R+h)

2

GM

----- (ii)

divide, (ii) by (i)

g

g

′

=

(R+h)

2

R

2

g

′

=

(R+h)

2

gR

2

For h<<<R,

g

′

=g(1−

R

2h

)