Proof Of Theory Of Relativity

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Albert Einstein introduced the special theory called the theory of relativity. He applied mathematics to give proof to this theory. The equation for theory of relativity is E=mc2. The main postulates of theory of relativity are: the speed of light is constant for all those who observe it and the observers who are moving at constant speeds should have the same physical laws. Theory of relativity can be proved by doing some experiments. Nuclear weapons are build on the basis of theory of relativity.
Mathematical Proof of Theory of Relativity :

The theory of relativity follow certain principles.Those are the speed of light is constant in vacuum and physics laws are same in all inertial frames.Einstein derived an equation in theory of relativity is E=mc2.In this theory the mass can be changed with respect to speed.

The mass increases with respect to increase in speed is shown in the following equation :

m = (m_0)/(sqrt(1-(v^2/c^2)))

From the above equation ,

m is the mass of object which is in travelling
m0 mass of object which is at rest,
v is the object speed
c is the ...
... light speed

The speed of the object increases its mass also get increased.The formula for kinetic energy is

E= 1/2 mv^2

The kinetic energy and mass increases due to motion.Therefore

E = mc^2 + 1/2 mv^2

This equation can be rearranged as

E-mc^2 = 1/2mv^2

The mass increases due to speed to light is equal to relative kinetic energy as

Relative kinetic energy= E-mc2

E=Relative kinetic energy + mc2

The object is at rest so the kinetic energy is zero.Then the equation becomes

E= 0 + mc2

Therefore, E = mc^2

From the above proof, Einstein said that the mass and energy are same.This can be shown in following graph.

Check this Subtracting Fractions Calculator awesome i recently used to see.

Example- Proof of Theory of Relativity:

1.Let the mass of the body be 50kg.Using the Einsteins theory of relativity find the energy required to move the body.

[Hint :speed of light = 3 * 108 m/s]

The solution is

The given mass m = 50 , c=3 * 10 8 m/s

E = mc2

= 50 * 3 * 108

= 150 * 108

=15* 109 m/s

In mathematics, change of variable theory is represent as x'. Here x' is indicate the change of the variable x. It is also called as differentiation of the variable. Or variable is a symbol that also can stand for a value that can be vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, that is completely fixed. Here we are going to learn about variable change theory.
Model Problems of Variable Change Theory:

Example 1:

Calculate the rate of change of the given function f(x) = 4x2 - 27x with respect to the variable x.

Solution:

Step 1: The given function is f(x) = 4x2 - 27x

Step 2: We need to calculate the rate of change of the function with respect to variable x, we get

f'(x) = 8x -27.

Step 3: Therefore, the answer is 8x - 27

Example 2:

Calculate the rate of change of the given function f(y) = 6y3 + 106y with respect to the variable y.

Solution:

Step 1: The given function is f(y) = 6y3 + 106y

Step 2: We need to calculate the rate of change of the function with respect to variable x, we get

f'(y) = 18y2 + 106

Step 3: Therefore, the answer is f'(y) = 18y2 + 106

These are the example problems of variable change theory.
Some more Examples of Variable Change Theory:

Example 3:

Calculate the change of variable x for the function c = 7x4 – 13x2 + 34x

Solution:

Step 1: The given function is c' = 7x4 – 13x2 + 34x

Step 2: We need to calculate the rate of change of variable x.so, we get c' = 7x3 – 26x + 34

Step 3: Therefore, the answer is c' = 21x3 – 26x + 34

Example 4:

Calculate the change of variable y for the function x = 1y4 – 4y2 + 145y

Solution:

Step 1: The given function is x' = 1y4 – 4y2 + 145y

Step 2: We need to calculate the rate of change of variable x.So, we get x' = 4y3 – 8y + 145

Step 3: Therefore, the answer is x' = 4y3 – 8y + 145.

These are the example problems of variable change theory.

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