I E Irodov Physical Fundamentals Of Mechanics (Relativistic Mechanics) Q. 1.350

I E Irodov Physical Fundamentals of Mechanics is one of the most recommended Physics books for students preparing for JEE Advanced, Physics Olympiads and other competitive examinations.

This chapter on Relativistic Mechanics introduces more advanced concepts of length contraction, dilation of time, Lorentz transformation and relativistic motion. These problems help students to develop good conceptual understanding and analytical thinking skills.

This page contains detailed solution of I E Irodov Physical Fundamentals of Mechanics (Relativistic Mechanics) Question 1.350 with explanation of concepts and formulae used.

I E Irodov Relativistic Mechanics Question 1.350

Question:

Two rods with equal proper length l_0 move towards each other parallel to a common horizontal axis.

In the frame of reference attached to one of the rods the time between the moments when the right ends and the left ends of the two rods coincide is Δt.

Find the velocity of one rod relative to the other.

Concepts Used in I E Irodov Q. 1.350

This question is based on the Special Theory of Relativity.

Important concepts involved are:

• Proper length
• Length contraction
• Relative velocity
• Lorentz factor
• Time interval
• Reference frames

The problem demonstrates how the observed length of a moving rod changes depending on the observer’s frame of reference.

Easy Solution of I E Irodov Relativistic Mechanics Q. 1.350

Given:

• Proper length of each rod = l₀
• Time interval = Δt
• Relative velocity = v (to be found)

Since we are observing from the frame fixed to one rod,

• One rod remains at rest.
• The other rod moves with velocity v.

Step 1: Length of the Moving Rod

The stationary rod has its proper length:

[
L_1=l_0
]

The moving rod undergoes length contraction.

Therefore,

[
L_2=l_0\sqrt{1-\frac{v^2}{c^2}}
]

Step 2: Distance Travelled During Coincidence

Initially, the front ends of the rods coincide.

After time Δt, the rear ends coincide.

During this interval, the moving rod travels a distance equal to the sum of the two visible lengths.

Therefore,

l_0+l_0\sqrt{1-\frac{v^2}{c^2}}
]

or

l_0
\left(
1+\sqrt{1-\frac{v^2}{c^2}}
\right)
]

Step 3: Rearranging the Equation

Divide both sides by l₀:

1+\sqrt{1-\frac{v^2}{c^2}}
]

Move 1 to the left side:

\sqrt{1-\frac{v^2}{c^2}}
]

Now square both sides.

After simplification, the required relative velocity satisfies

[
\boxed{
v=
\frac{2l_0c^2\Delta t}
{c^2(\Delta t)^2+l_0^2}
}
]

This is the required velocity of one rod relative to the other.

Final Answer

The relative velocity of the rods is

[
\boxed{
v=
\frac{2l_0c^2\Delta t}
{c^2(\Delta t)^2+l_0^2}
}
]

Simple Explanation of the Answer

One rod is fixed and the second rod moves towards it.

The moving rod is contracted in length . This means its length as seen by the observer is less than its proper length .

In the time allowed the moving rod sweeps the entire visible length of both rods.

Then we can use the length contraction formula and the relation between distance velocity and time to get the required expression for relative velocity.

The solution demonstrates the relation between the proper length, length contraction and relative motion in Special Relativity.

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Key Takeaways

Common Mistakes Students Should Avoid

Students commonly make these mistakes:

• Using the proper length for both rods.
• Forgetting that only the moving rod undergoes length contraction.
• Using classical mechanics instead of relativistic formulas.
• Confusing the stationary frame with the moving frame.
• Ignoring the Lorentz factor while calculating the contracted length.

Always identify which object is stationary before applying the length contraction formula.

Why Practice I E Irodov Problems for JEE Advanced?

I E Irodov problems help students develop advanced Physics concepts beyond routine JEE problems.

Benefits include:

• Deep conceptual comprehension

Improved analytical thinking

Better mathematical implementation

Confidence in advanced numeracy problems

Better preparation for JEE Advanced and Physics Olympiad

Students should solve selected I E Irodov problems only after mastering NCERT concepts, JEE Main questions and JEE Advanced level Physics.

Is I E Irodov Q. 1.350 a JEE Main Question?

Nope. Q. 1.350 I E Irodov Relativistic Mechanics is not a usual JEE Main level problem.

This question is based on the Special Theory of Relativity and involves understanding the concepts of length contraction, proper length, Lorentz factor and relative motion. These ideas are typically studied in advanced Physics preparation.

This question is recommended for:

• JEE Advanced aspirants
• Physics Olympiad students
• Students interested in advanced mechanics
• Learners who have completed the standard JEE Physics syllabus

If you are preparing for JEE Main, start with NCERT, standard JEE level numerical problems, previous year papers and mock tests before you start referring advanced reference books like I E Irodov.

Is Relativistic Mechanics Important for JEE?

Relativistic Mechanics is not a high weightage chapter in JEE Main. But it helps students to build up the advanced Physics concepts required for the JEE Advanced.

Students learn important topics like:

• Special Theory of Relativity
• Proper Length
• Length Contraction
• Lorentz Transformation
• Time Dilation
• Relative Velocity
• Mass-Energy Relation

Only a few questions are based on relativity, but if you understand these concepts, your problem solving ability will improve overall.

Important Topics in I E Irodov Physical Fundamentals of Mechanics

How Should Students Use I E Irodov for JEE Advanced?

The best way to use I E Irodov is after building strong Physics fundamentals.

Recommended preparation strategy:

This approach helps students understand advanced concepts without becoming overwhelmed.

I E Irodov for NRI JEE Students

Selected I E Irodov questions are very useful for NRI students from USA, UAE, Saudi Arabia, Qatar, Oman, Kuwait and Bahrain preparing for JEE Advanced.

Students appearing for AP, IB, British or any other international boards must first complete the JEE syllabus and then solve advanced reference books.

Recommended preparation sequence:

• Complete the JEE Physics syllabus
• Solve chapter-wise JEE questions
• Practice JEE Main previous year papers
• Solve JEE Advanced previous year questions
• Attempt selected I E Irodov problems
• Revise concepts and formulas regularly

This structured approach helps NRI students strengthen conceptual understanding and advanced problem-solving skills.

Related I E Irodov Relativistic Mechanics Questions

After completing Question 1.350, students can also practice:

• I E Irodov Relativistic Mechanics Q. 1.345
• I E Irodov Relativistic Mechanics Q. 1.359
• I E Irodov Relativistic Mechanics Q. 1.378
• I E Irodov Relativistic Mechanics Q. 1.388

Link each question to its corresponding TestPrepKart solution page to improve concept continuity.

Practice Next

After solving this question, students should continue with:

• Relativistic Mechanics numerical problems
• Length Contraction questions
• JEE Advanced Physics previous year papers
• Mechanics revision notes
• Modern Physics practice questions
• JEE Advanced mock tests

Regular practice of advanced numerical problems improves analytical thinking and conceptual understanding.

Useful JEE, DASA & CIWG Resources for I E Irodov Physics

FAQs on I E Irodov Relativistic Mechanics Q. 1.350

1. What is the main concept used in I E Irodov Q. 1.350?

The problem is based on length contraction, proper length and relative motion in Special Relativity.

2. Is I E Irodov Q. 1.350 useful for JEE Main?

This question is above the usual JEE Main level and is mainly recommended for JEE Advanced preparation.

3. Why is only one rod length-contracted?

Length contraction occurs only for the rod moving relative to the observer. The rod at rest in the chosen reference frame keeps its proper length.

4. Which formula is most important in this question?

The most important relation is the Lorentz length contraction formula:

[
L=L_0\sqrt{1-\frac{v^2}{c^2}}
]

5. Is this question suitable for beginners?

No. Students should first complete Mechanics, Modern Physics and JEE-level questions before attempting advanced relativity problems from I E Irodov.

6. Is I E Irodov useful for JEE Advanced?

Yes. Selected I E Irodov problems help students strengthen advanced Physics concepts and improve their performance in JEE Advanced.