Question

Derive acceleration due to gravity on earth

Answer 1

Answer:

Formula of Acceleration due to Gravity

Force acting on a body due to gravity is given by, f = mg

Where f is the force acting on the body, g is the acceleration due to gravity, m is mass of the body.

According to the universal law of gravitation, f = GmM/(r+h)2

Where,

f = force between two bodies,

G = universal gravitational constant (6.67×10-11 Nm2/kg2)

m = mass of the object,

M = mass of the earth,

r = radius of the earth.

h = height at which the body is from the surface of the earth.

As the height (h) is negligibly small compared to the radius of the earth we reframe the equation as follows,

f = GmM/r2

Now equating both the expressions,

mg = GmM/r2

⇒ g = GM/r2

Therefore, the formula of acceleration due to gravity is given by, g = GM/r2

Note: It depends on the mass and radius of the earth.

This helps us understand the following:

All bodies experience the same acceleration due to gravity irrespective of its mass.

Its value on earth depends upon the mass of the earth and not the mass of the object.

Answer 2

Answer:

Modelling the Earth as a symmetric, spherical body (and by using the law of gravitation), we come up with the equation

w=F=GMm/R^2

ma = GMm/R^2

a=g

g=GM/R^2

Where:

G=gravitational constant=6.67×10−11 N

M=mass of Earth=5.98×1024 kg

R=Earth's radius=6380 km