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We have all witnessed gravity in action at some point in our lives. After all, it is the power that keeps our feet firmly planted on the earth. If we throw a ball in the air in an upward motion. It will then fall on its own. Why? When the ball is moving upwards, its speed will be slower than when it is moving downwards. Because of the acceleration caused by gravity’s force, this is the case. The acceleration due to the gravity formula will be discussed in this topic. Let’s take a closer look at gravity’s acceleration.
The formula for Acceleration Due to Gravity
Newton’s Second Law of Motion and Newton’s Law of Universal Gravitation are used to calculate the acceleration due to gravity. These two principles combine to give the most practical form of the formula for determining gravity acceleration: g = G*M/R2, where g denotes gravity acceleration, G the universal gravitational constant, M mass, and R distance. The rest of this lesson expands on this formula, clarifies its meaning, and provides practical examples of its application in determining acceleration due to gravity.
The formula for the acceleration due to gravity at a depth of h
The value of g decreases as the distance from the earth’s surface increases. We’ll talk about and derive the equation that shows how the value of g changes as you get farther away from the earth’s surface.
Formula= g2 = g (1 – h/R).
The acceleration due to gravity at depth h is given by g2, while the radius of the earth is given by R.
The acceleration owing to gravity on the earth’s surface is denoted by the letter g.
For example, if g = 9.8 m/s2 on the surface of the earth, g2 at 1000 metres below the surface of the earth becomes 9.7984 m/s2.
Gravitational Acceleration Formula
The formula of acceleration due to gravity is nearly constant at the Earth’s surface. The acceleration is different at considerable distances from the Earth, or around other planets or moons. Gravitational acceleration is determined by the mass of the body, its distance from the centre of mass, and a constant G, also known as the “universal gravitational constant.” = 6.673 x 10-11 Nm2/kg2 is its value.
Variation of g with height and depth
The formula of acceleration due to gravity, or g, varies as the height or depth of a person is measured about the earth’s surface. This means that the value of g on top of a mountain will differ slightly from that on the ground. Similarly, the value of g at a depth below the earth’s surface will not be the same as the value of g at the surface. The fluctuation of g with height and depth is known as g variation.
The formula g1 = g (1 – 2h/R)———-(1) expresses the variation of g with height.
The formula g2 = g (1 – d/R)———(2) expresses the variation of g with depth.
The formula of acceleration due to gravity at a height of h above the earth’s surface is denoted by g1. And, concerning the earth’s surface, g2 is the acceleration due to gravity at depth d. The radius of the earth is R.
The magnitude of the fluctuation of g with height differs from that of g with depth. However, it’s worth noting that the value of g decreases with increasing height and depth about the earth’s surface. This also indicates that the value of g is greatest on the earth’s surface.
Now, to discuss how gravity’s acceleration changes with height and depth on the earth’s surface, we’ll use simple mathematics to analyse (1) the variation of g with height and (2) the variation of g with depth separately, and derive the formulas that describe this variation of g with altitude and depth.
Variation of g with height: The value of acceleration owing to gravity decreases as altitude or height h above the earth’s surface increases. The formula g1 = g (1 – 2h/R) is used to express this. The acceleration due to gravity at a height of h above the earth’s surface is g1, and the radius of the earth is R.
As a result, the value of g decreases by this amount at a height h above the earth’s surface: 2gh/R.
The formula for g at height h
The formula g1 = g (1 – 2h/R) expresses the variation of g with height. The acceleration due to gravity at a height of h above the earth’s surface is g1, and the radius of the earth is R.
Variation of g with depth: The value of acceleration due to gravity decreases as the depth d below the earth’s surface increases. The formula g2 = g (1 – d/R) is used to express this. Here, g2 is the gravitational acceleration at depth d concerning the earth’s surface, and R is the earth’s radius.
As a result, the value of g falls by this amount at a depth d below the earth’s surface: gd/R
The formula for g at depth d
The formula g2= g (1 – d/R) expresses the variation of g with depth. Here, g2 denotes the acceleration due to gravity at a depth of d from the earth’s surface, and R denotes the earth’s radius. The formula for g at depth d is as follows.
Conclusion
When falling freely under the influence of gravity at the same point on the Earth, all things, regardless of mass, experience the same acceleration g. g=9.8 m s2 near the Earth’s surface.
