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Acceleration due to Gravity

Let us understand the concept of acceleration due to gravity and the properties exhibited by the concept and its application in real life.

Define Acceleration due to Gravity

The acceleration due to gravity refers to the acceleration and speed gained by an object due to the gravitational pull exerted by the gravitation on it. It is always calculated in m/s2. Gravitation is a vector quantity as it has both direction and magnitude. The acceleration due to gravity is always represented as “g”, and on the earth’s surface, its value is 9.8 m/s2.

Acceleration due to Gravity – Formula, Unit, and Values

Acceleration Due to Gravity (g)

Symbol g
Dimensional Formula M0L1T-2
SI Unit ms-2
Formula g = GM/r2
Values of g in SI 9.806 ms-2
Values of g in CGS 980 cms-2

What is Gravity

The term gravity refers to the force exerted by the earth on the object, pulling it towards the earth’s center. To understand the gravity, let us consider this example below:

Suppose we have two bodies of masses that are ma and mb. According to the application of equal forces on the given two bodies, the force in order of mass is given as:

mb = ma [aa/ab] is renowned as the body’s inertial mass.

Under the gravitational influence exerted on two bodies,

• Fa = GMma/r2
• Fb = GMmb/r2
• mb = [Fb/Fa] × ma

The mass referred to in the above example is the body’s gravitational mass. As stated in the law of equivalence, the inertial mass and the gravitational mass are always identical. This is mostly used while deriving the acceleration due to gravity.

Derivation of Acceleration due to Gravity

To understand the derivation with ease, let us assume the following:

Suppose a body of mass (m) is dropped from the height ‘h’ somewhere above the surface of the earth mass (M); as it begins to move towards the earth, the velocity shoots up.

We are aware that the velocity of an object changes only under one circumstance, that is, the action of a force; in our case stated above, the force is being provided by gravity.

Under the influence of gravitational force, the object starts to accelerate toward the earth’s center, which is at a distance ‘r’ from the given test mass.

From this we understand, ma = GMm/r2 (Applying the principle of equivalence)

⇒ a = GM/r2 . . . . . . . (1)

The above acceleration is due to the influence of the earth’s gravitational pull, so we recall it as acceleration due to gravity; it does not depend upon the test mass. Its value near the surface of the earth is always 9.8 ms-2.

The acceleration (g) calculated is written as = GM/r2.. . . . . (2)

Formula of Acceleration due to Gravity

Gravitational acceleration formula is given by the following:

The force acting on a body because of gravity is always given by F = mg

Here, f is the force acting on the body, g is the gravitational acceleration, m is the mass of the given body.

According to the universal law of gravitation provided by Newton, F = GmM/(r+h)2

Where,

• F is equivalent to force between two bodies
• G is equivalent to the universal gravitational constant (6.67×10-11 Nm2/kg2)
• m is equivalent to a mass of the object
• M is equivalent to the mass of the earth
• r is equivalent to the radius of the earth
• h is equivalent to the height of the body from the earth’s surface

Certain factors can influence the acceleration:

It urges on the mass and radius of the earth, like

• All bodies on the surface of earth freely falling experience the same acceleration due to gravity, irrespective of their mass
• Its value on earth fluctuates or changes due to the mass of the earth and not because of the mass of the object

Acceleration due to Gravity on the Earth’s Surface

Earth is assumed as a uniform solid sphere with a density.

We know that,

Density = mass/volume

Then, ρ = M/[4/3 πR3]

⇒ M = ρ × [4/3 πR3]

From previously learned concepts, we know, g = GM/R2.

On substituting the values of M from the above-stated equations, we get,

g = 4/3 [πρRG]

At any taken distance ‘r’ from the center of the earth

g = 4/3 [πρRG].

The value of the acceleration due to gravity ‘g’ is also affected by some factors that are:

• The altitude of an object above the earth’s surface
• The depth below the earth’s surface
• The shape of the earth
• Rotational movement of the earth

Important Conclusions on Acceleration due to Gravity :

• For the object placed at the height of ‘h’, the acceleration due to gravity is always less than the object placed on the surface
• As depth increases, there is a fall in the value of acceleration due to gravity (g)
• The value of g is greater at poles and less at the equator

Conclusion

The above article enlightens us about acceleration due to gravity, its concept, and its definition. It is referred to as the acceleration and speed gained by an object due to the gravitational pull exerted by the gravitation on it. It is always calculated in m/s2. Gravitation is a vector quantity as it has both direction and magnitude. The acceleration due to gravity is always represented as “g” and on the earth’s surface its value is 9.8 m/s2.

Get answers to the most common queries related to the JEE Examination Preparation.

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