Question

assuming earth to be a sphere of radius R. At what altitude will the value of acceleration due to gravity will be half of its value at the surface of the earth?

plsss!!!answer fast

Answer 1

Answer:

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

Explanation:

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