The acceleration due to gravity is 2.5 m/s^2 at heigth h from the surface of earth. If diameter of earth is d then the magnitude of H is equal to
[Take g = 10 m/s^2]
d
d/3
d/2
2d
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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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