Question

How does $E=m{c}^2$ work?

Answer 1

Hint: In Physics, we study the frame of reference. The speed of an object is different in a different frame of reference, depending on the motion of the observer. This leads to the fact that kinetic energy will also be dependent on the reference frames and observer motion. We have two types of reference frames, Inertial frames, those moving with constant or zero acceleration, and non-inertial, those moving with variable acceleration.

Complete answer:
Let us understand the meaning of a few terms here.
The rest mass of an object is the mass in its rest frame and it is the same for all inertial frames of reference. Relativistic mass is the variable mass of an object which changes for different observers.
It is seen that the relativistic mass when the object is in motion is greater than the relativistic mass when the object is at rest. At very high speed the relativistic mass of the object is equal to relativistic energy divided by $c^2$.
$m_{relativistic}={\displaystyle \frac{E}{c^2}}$
Nuclear binding energy is the minimum energy required to separate the nucleus into its components.
We know that the mass of an atom is less than the mass of its constituent particle, this difference in mass is called mass-defect. It is calculated by energy-mass relation, $\mathrm{\Delta }m{c}^2$.
This energy-mass relation is used for modeling nuclear fission reactions.

Note:
As we now have the idea of reference frames, we understood that the measurement is dependent on the motion of the observer and energy will depend on the observer. The relativistic energy is given by the product of relativistic mass and $c^2$(speed of light). So, the relativistic mass and energy are directly proportional, almost the same, only units are different.