Question 157: Gravitation

Question

The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).

Accepted Answer

The acceleration due to gravity (g) at a distance (r) from the center of a planet is given by:
$$g = \frac{G M}{r^2}$$
where:
G is the gravitational constant,
M is the mass of the planet,
r is the distance from the center of the planet.
If the height h of a point P above the surface of the Earth is equal to the diameter of the Earth, then the distance r from the center of the Earth to the point P is 3 times the radius of the Earth. Substituting this into the equation for g gives:
$$g' = g \left(\frac{R}{3R}\right)^2 = \frac{g}{9}$$
where:
g' is the acceleration due to gravity at the point P,
R is the radius of the Earth.
Therefore, the value of acceleration due to gravity at point P is g/9.

Answer

g/2

Answer

g/4

Answer

g/3

Answer

g/9

Gravitation

The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).

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