Question

prove it e=mc square

Answer 1

to prove it you must know about special relativity which was proposed by Albert Einstein.

let's say you're conducting an experiment in space. you have a radioactive dog in space and it's emitting a flash of light in all directions symmetrically. now as the dog is emitting light it must be losing energy equal to the energy of light emitted. as the energy is emitted symmetrically it will not change the dog's velocity. let's name the energy emitted as E .

now let's imagine that you get bored and zoom off in a spaceship traveling close to the speed of light. let's call that velocity v. now by your perspective you are standing still but the dog is the one which passes you away at the velocity v. you will see it gain some kinetic energy lets call it KE1 and by Einstein's theory of relativity time passes at different rates for the dog and you. Thus you'll measure a different frequency of light as frequency is 1/ time period. when you'll see the dog emit the flash of light while in the spaceship you'll measure the energy of light emitted by multiplying E with (1+ V²/2c²) where c is the speed of light. now you'll see the dog losing energy by E.(1+v²/2c²).

let's assume you wait and let the dog emit the flash of light and then zoom off. you'll see the dog lose energy by E then gain kinetic energy called KE2. now here's when we meet the problem. we haven't touched or influenced the dog in any way so the total energy must be the same at the end.

for more information refer minutephysics' video on the proof

-E + KE2 = KE1- E.(1+v²/2c²)
-E+KE2 = KE1-E+E.v²/2c²
cancelling -E on opposite sides of the equation
KE2=KE1+ E.v²/2c²

from this it is clearly visible that KE1 is not equal to KE2. and we know that velocity is the same so the changes in kinetic energy must've come from change in dog's Mass.
as KE = 1/2 mv²
1/2m1v²= 1/2m2v²+E.v²/2c²
1/2v²m1=1/2v²( m2 + E/c²)
cancelling 1/2 v²
m1= m2+ E/c²
m1- m2 = E/c²
substituting m1-m2 by ∆m(change in Mass)
∆m=E/c²
and.....
E = (∆m)c²

hence proved

Answer 2

Theory of relativity.

In the year 1929 a famous mathematician and physicist named Albert Eisenstein gave a theory which shows relation between time and motion.

yes i am talking about special theory of relativity.

actually theory of relativity is divided in two parts

1. special theory of relativity

and

2. general theory of relativity.

✔special theory of relativity is based on the time and motion.

there are two frame of references.

1. inertial frame of reference

and

2. inertial frame of reference.

in inertial frame of reference we talk about when body is moving with constant velocity.

and

in non inertial frame of reference we talk about unconstant velocity.

in the special theory it is used that the time and motion are relative.

and there is a postulate that

✳ Nothing can travel faster than the speed of light that is.

299692458m/s and universe is limited at this speed so if a object moves near the speed of light then the time slows down for that object in order to maintain that speed.

Now

Theory of general relativity.

✔ after giving special relativity Einstein was not satisfied and wanted to know about how gravitational force can affect time.

so he gave general theory of relativity.

in this we talk about the gravitational force.

space time curvature

fabric of cosmos and many more thing

in this Einstein showed that how gravitational force affect the time and also showed that the planets revolve around the sun because of the curve in space time