How does value of 'g' on earth is related to mass of earth and radius. Derive it.
Answers
The value of g is influenced by the mass and radius of earth as g is acceleration of an object due to earth's gravitational force. The earth pulls everything on its surface towards its centre,so the distance between the centre and the object which is indirectly the earth's radius,has to be considered.
The more distance between the object and the earth, the lesser will be the force of gravity on it.
So g=Mm/r^2
M is the mass of earth
m is the mass of object
r is radius of earth
Hope it helps.
Answer:how does the value of ‘g’ on earth related to mass of earth and radius. Derive it
Explanation:
Consider a body of mass ‘m’ held at a distance of ‘r’ from the center of the earth (radius of earth =R) of mass ‘M’
According to Newton’s law of gravitation:
F=Gm1m2/r*2
F=GmR/R*2. .........(1)
Acc. To Newton’s second law of motion
F=mg. .........(2)
From equations (1) and (2)
GmM/R*2=mg
(m and m cancels)
GM/R*2=g
6.67*10*-11*6*10*24/6.4*10*6
=9.77~ approx 9.8
Hence,g= 9.8m/s*2