Question

Define acceleration due to gravity .Deduce an expression for it in terms of mass of the Earth (M) and universal gravitational constant (G)

Answer 1

it is the acceleration produced in an object, when it is falling towards the centre of the earth, only under the influence of gravity.

consider an object of mass 'm 'lying at the surface of the earth.

from universal law of gravitation;

F = GMm/r^2 ----e1  (as the object is on the surface of the earth, 'd' becomes 'r'.)

from newtons second law of motion;

F = mg ------e2

from e1 and e2;

mg = GMm/r^2

(we remove ''m' from both sides.)

therefore, g = Gm/r^2

value of 'g' on the surface of the earth = 9.8 m/s^2

Answer 2

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