Question

What does it mean to say that the gravity of the Earth is $9.8m{s^{ - 2}}$?

Answer 1

To answer this question we will first know what force is , what acceleration due to gravity is an then we will apply a formula that relates force mass and acceleration as given by Isaac Newton and at last we will tell what we mean by gravity of earth is $9.8m{s^{ - 2}}$.

Formula Used:
F=MA
Where F=force , A= acceleration
And M= mass

Complete step-by-step solution:
Gravity is a force, and Newton's Second Law states that when a force acts on an object, it accelerates:
F=MA
Acceleration is a rate of change of speed (or velocity, if working with vectors). Speed is measured in $m{s^{ - 1}}$, so a rate of change of speed is measured in $\dfrac{{m{s^{ - 1}}}}{s}$ or $m{s^{ - 2}}$.
We can't truly talk about the "force of gravity" being a constant because a large object will experience a great force of gravity and a tiny object will feel a little force of gravity. The "gravitational field strength" is defined as the amount of gravitational force per kilogram of mass that is $\left( {9.8\dfrac{N}{{kg}}} \right)$ , However, the Newton (N) is a derived unit, which means $1N = 1kgm{s^{ - 2}}$, so $\dfrac{N}{{kg}}$ is really the same thing as $m{s^{ - 2}}$ anyway.
It's worth noting that gravity isn't constant; as you travel further out from the Earth's centre, gravity becomes weaker. It fluctuates from 9.83 at the poles to 9.78 at the equator, therefore it isn't even a constant at the surface. This is why the average value of 9.8, or 9.81, is used.

Note: Another way to answer this question in simple words would be: The velocity of an object changes when it falls freely towards the earth's surface from a specific height. The object accelerates as a result of the change in velocity, which is known as acceleration due to gravity, indicated by the letter ‘g’. $g = 9.8{\text{ }}m{s^{ - 2}}$ is the value of gravity acceleration.