Question

I have to write a lab report on "Measuring the value of g". For the theory section, I have to predict my theoretical value for "g " and its uncertainty. Explain how did I arrive to those numbers (do not quote someone else's value for "g").

Does anyone have an idea of how can I do this? Thanks a lot.

Answer 1

Bodies allowed to fall freely were found to fall at the same rate irrespective of their masses (air resistance being negligible). The velocity of a freely falling body increased at a steady rate, i.e., the body had acceleration. This acceleration is called acceleration due to gravity'g'.

We know,

From Newtons Second Law,
F = mg ............ (1)

Equation of Force is given by Newton's law of gravity, which states that every point mass in the universe is attracts to every other point mass in the universe with a force which is directly proportional to the product of their masses and inversely proportional to square of the distance between them. It can be written as,
F = GMmR2 .............(2)

Where
F is the force,
m is the mass of the body,
g is the acceleration due to gravity,
M is the mass of the Earth,
R is the radius of the Earth and
G is the gravitational constant

By knowing these constants, we can calculate acceleration due to gravity theoretically. From equations (1) and (2), we can also conclude that 'g' varies with
(a) Altitude
(b) Depth and
(c) Latitude.