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Revision Notes: Relativity | Mock Tests for JEE Main and Advanced 2025 PDF Download
- Frame of reference:- A system of coordinates whose axes can be suitably chosen is said to be a frame of reference.
- Inertial frame:- A frame of reference either at rest or moving with a uniform velocity (zero acceleration) is known as inertial frame.
- Non-inertial or accelerated frame:- It is a frame of reference which is either having a uniform linear acceleration or is being rotated with a uniform speed.
- Galilean transformation:-
(a) Transformation of position:-
x' = x – vt
y' = y
z' = z
t' = t
Inverse transformation,
x = x'+ vt '
y = y'
z = z'
t = t'
(b) Transformation of distance:-
l ' = l
Here, l = x2-x1 is the length of rod as observed in frame S.
Anything which remains unchanged when observed from the two Galilean frames of reference is known as Galilean invariant.
(c) Transformation of velocity:-
u'= u– v
Inverse transformation:- u = u'+ v
(d) Transformation of acceleration:-
a' = a
Thus, the acceleration of body, as observed by two observers siting in two inertial frames, is same. Hence, acceleration is said to be Galilean invariant. - Law of conservation of momentum:-
It states that the total momentum of an isolated system (no external force) always remains constant.
In S frame:- m1u1 + m2u2 = m1v1 + m2v2
In S ' frame:- m1u'1 + m2 u'2 = m1 v'1 + m2 v'2
Thus, the law of conservation of momentum is valid in S ' also, indicating that the law is Galilean invariant. - Ether and velocity of light:- c' = c ±v
- Postulates of special theory of relativity:-
(a) The laws of physical phenomenon are same when stated in terms of two systems of reference in uniform translator motion relative to each other.
(b) The velocity of light in vacuum is constant, independent not only of the direction of propagation but also of the relative velocity of the source and the observer. - Lorentz transformation equations:-
x' = [x - vt]/√[1- v2/c2]
y'= y
z'= z
t' = [t – [(v/c 2) x]]/√[1- v2/c2] - Lorentz inverse transformation equations:-
x= [x' + vt] /√[1- v2/c2]
y = y'
z= z'
t= [t' + [(v/c2) x']]/√[1- v2/c2] - Length contraction:-
l = l0√[1- v2/c2]
So, l<l0
Here, l0 is the proper or original length in S frame and l is the relativistic length in S' frame. - Time Dilation:-
??t = ??t0/√ [1-v2/c2]
So, ?t > ??t0
Here, ??t0 is the proper or original time in S frame and ?t is the relativistic time in S' frame.
?Thus, the time interval as observed by the moving observer appears to be lengthened. - Frequency:- If f0 is the natural frequency of a process in frame S, then the frequency f as observed from S ' given by,
f = f0√[1- v2/c2] - Relativistic velocity addition theorem:-
ux' = [ux – v]/[1- [(v/c2)ux]]
uy' = [uy√[1- v2/c2]]/[1- [(v/c2)ux]]
uz' = [uz√[1- v2/c2]]/[1- [(v/c2)ux]] - Relativistic variation of mass:-
m= m0/√[1-v2/c2] - Rest mass energy:-
E0 = m0c2 - Total energy (Mass-Energy Equivalence):-
E= mc2 = [m0/√[1-v2/c2]] c2 - Kinetic energy:-
EK= E - E0 = (m - m0) c2
Here c is the speed of light, m0 is the rest mass and m is the relativistic mass. - Relativistic momentum:-
p= mv
= [m0/√[1-v2/c2]] v
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FAQs on Revision Notes: Relativity - Mock Tests for JEE Main and Advanced 2025
| 1. What is the theory of relativity? |  |
Ans. The theory of relativity, proposed by Albert Einstein, is a scientific theory that describes the relationships between space and time, and how they are affected by gravity. It includes two main parts: the theory of special relativity, which deals with objects moving at constant speeds in the absence of gravity, and the theory of general relativity, which incorporates the effects of gravity.
| 2. How does the theory of relativity explain time dilation? | |
Ans. According to the theory of relativity, time dilation occurs when an object is moving at a high velocity or in a strong gravitational field. This means that time passes slower for objects in motion or near massive objects compared to objects at rest or in weaker gravitational fields. This phenomenon has been experimentally observed and is an essential aspect of the theory of relativity.
| 3. Can you provide an example of the theory of relativity in action? | |
Ans. One famous example of the theory of relativity in action is the observation of gravitational lensing. This occurs when light from a distant object is bent by the gravitational field of a massive object, such as a galaxy or a black hole. The bending of light is a direct consequence of the curvature of spacetime predicted by the theory of general relativity.
| 4. How does the theory of relativity relate to the concept of space-time? | |
Ans. The theory of relativity combines the three dimensions of space (length, width, and height) with the dimension of time to form a four-dimensional framework known as space-time. It suggests that space and time are interconnected and that they can be influenced by gravity. The theory of relativity describes how objects move and interact within this unified space-time framework.
| 5. What are the practical applications of the theory of relativity? | |
Ans. The theory of relativity has several practical applications in modern technology. For example, it is essential for the accurate functioning of the Global Positioning System (GPS), which relies on precise timing and takes into account the time dilation effects caused by the satellites' motion in space. Additionally, the theory of relativity has led to advancements in astronomical observations, space exploration, and the development of atomic clocks.
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