The acceleration due to gravity at the surface of the earth (mass M and radius R) is proportional to __________.

Question

Question

This question was previously asked in

RRB ALP CBT I 17 Aug 2018 Shift 3 Official Paper

Answer 1

The correct answer is M/R².

Key Points

The force acting on an object due to gravity is given by f = mg.
Where f is the force acting on the object, g is the acceleration due to gravity, and m is the mass of the object.
According to the law of universal gravitation,
f = GmM/(r+h)².
Where,
f = force between two bodies,
G = universal gravitation constant (6.67×10-11 Nm2/kg2)
m = mass of an object,
M = mass of earth,
r = radius of the Earth.
h = height the object is from the earth's surface.
Since the height (h) is negligible relative to the radius of the earth, we repeat the equation as follows,
f = GmM/r2
Now balance the two expressions,
mg = GmM/r2
⇒ g = GM /r2
Therefore, the formula for the acceleration due to gravity is given by, g = GM/r²