Question

Acceleration due to gravity formula derivation

Answer 1

Hey dear ‼‼

So here's your answer :-

✴Let us drop an object (say a stone) of mass "m" from a distance "r" from the centre of the earth of mass "M". Then the magnitude of force exerted by the earth on the stone is given by

↪F = G*M*m/ r^2........(i)

Where "G" is gravitational constant,
= 6.67*10^-11 Nm^2 kg-2.

The force exerted by the earth produces acceleration in the stone due to which the stone moves downwards.

✴We also know that second law of motion that force as the product of mass and acceleration, i.e.

✴ Force=Mass*Acceleration ✔
F=ma.

But the acceleration due to gravity is represented by the symbol 'g' in place of 'a' in the above equation, we get :-

F=mg .......(ii)

Comparing equations (i) & (ii), we get

mg = G*M*m/r^2.

or

g = G*M/r^2......(iii)

If the stone is on or near the surface of the earth, then distance in equation (iii) "r" is taken to be "R", the surface of the earth.

Thus , for objects on or near the surface of the earth,

g= G*M/ R^2........(iv)


Hope this helps you dear ✌

Answer 2

$\textbf{Answer is in Attachment !}$