Reference Notes | SLC
Gravity or Weight
For: Science Class 10

The force of attraction of the earth on a body is called force of gravity or simply the weight of the body on earth. Let a body of mass m be placed on the surface of the earth of mass M as shown in the figure. The distance between them can be taken to be equal to the radius (R) of the earth. The weight (W) of the body on the surface of the earth is given by:

Equation (ii) shows that weight (W) of a body on the surface of a planet/ satellite is directly proportional to mass (M) of the planet /satellite. Greater the mass of the planet /satellite, larger its gravity is i.e., greater will be the weight of the body on the planet/satellite.

Equation (ii) also shows that weight (W) of a body on the surface of a planet/satellite is inversely proportional to the square of the radius (R) of the planet/satellite. The weight of the body will be less if it becomes large.

Effects of gravity

1. We are able to stand up, run and perform other activities freely due to gravity of the earth.
2. Construction of building and bridges is possible due to the gravity of the earth.
3. There will be no atmosphere around the earth in the absence of gravity of the earth.
4. If a body is thrown upwards, its notion is opposed by gravity of the earth. So, it falls back to the earth.
5. Tides occur by the gravity of the moon on ocean water.

Acceleration due to gravity
Acceleration due to gravity is defined as the acceleration produced in a freely falling body due to the force of gravity of the earth towards its center. It is denoted by g and its average value is 9.8 m/s².

Relation between Radius and Gravity
Let M be the mass of the earth and R its radius, then the force of attraction on a body of mass m on its surface as given by the Newton’s Universal law of gravitation is:

F = G (Mm / r²) —————- (i)
But, the force with which the body is attracted towards the center of the earth is the weight of the body.
W = mg ————— (ii)
As (i) and (ii) represents the same force, we get:
F = W
Or, G (Mm/R²) = mg
Or, g = GM / R² ————— (iii)

This is the expression for the acceleration due to gravity. The value of g on the surface of the earth is:

1. Independent of mass of the body.
2. Depends on the mass of the earth and the radius.
3. Suggests that the value of g at a particular place is constant.

Variation in the value of g

1. Variation due to shape [ On the surface]
   g = GM / R² —————- (a)
2. Variation with height
   g₁ = g {R/(r+h)}² ————– (b)
3. Variation with depth
   g₁ = g(1 – x/R) ———— (c)