Question

Derive gravitational constant (g=9.8)

Answer 1

Explanation:

According to the Universal Gravitational Law,

Force α Masses of the objects [directly proportional]

Force is inversely proportional to the square of Distance between the objects

or F α 1/D²

Let the masses be M, and m

=> F α Mm/D²

To balance the proportionality, we multiply it by a constant G, called Gravitational Constant

F = GMm/D²

G = FD²/Mm = 6.6742 × 10-¹¹ Nm²/kg²

According to the universal law of gravity,

F=GMm/R2 ————(1)

From Newton’s second law of motion we can write –

g = F/m ———–(2)

Substituting equation (1) in (2) we get-

Fg = GFMm/R²m

⇒ g = GM/R²