Question

the acceleration due to gravity is 2.5m/s^2 at height h from the surface of earth if the diameter of the earth is d then the magnitude of h is

Answer 1

The gravitational force acting on mass m on the surface of Earth is

F=

R

2

GMm

mg=

R

2

GMm

g=

R

2

GM

gR

2

=GM.............(1)

where, g is acceleration due to gravity, G is gravitational constant, M is mass of Earth and R is radius of Earth.

Now, value of g at height h is

g=

(R+h)

2

GM

As per the problem,

2

g

=

(R+h)

2

GM

g(R+h)

2

=2gR

2

................from (1)

(R+h)

2

=2R

2

Taking roots from both sides, we get

R+h=

2

R

∴h=

2

R−R

∴h=(

2

−1)R