According to the universal law of gravitation the gravitational force on a small

Question

According to the universal law of gravitation the gravitational force on a small mass at the surface of the Earth is proportional to the product of the mass and the mass of the Earth and inversely proportional to the square of the distance between the mass and the center of the Earth. It is a well established fact that Newton's Second Law holds and also that within the limits of experimental uncertainty all masses that are tossed or dropped hi a laboratory located on the surface of the Earth experience the same constant vertical acceleration of ag = -9.8y m/s^2. (a) If the Earth's gravitational force on a mass depends on the distance between it and the center of the Earth why doesn't the magnitude of the acceleration of an object dropped from the ceiling of a laboratory increase as the object gets closer and closer to the floor of the laboratory? (b) If the Earth's gravitational force on an object is proportional to its mass, why isn't the acceleration of an object that is twice the mass double that of the original mass?

Explanation / Answer

a) gravitational force on mass = G Me m / (Re + h)^2

acceleration of mass = F/m = G Me / (Re + h)^2

Re = 6.73 x 10^6 m

whille h = 10^1 m to 10^2 m

h << <<<< Re

and Re +h = Re

so these small height value of Re + h doesn't change.

hence g OR Fg are constant for such heights.

b) Gravitational force = G Me m / R^2

from newton's 2nd law, Fnet = ma

so onbject.

Fnet = G Me m / r^2 = ma

a = G Me / r^2

this is independent of mass of object , hence it will be constant despite masses of objects.

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