I E Irodov Physical Fundamentals Of Mechanics (Relativistic Mechanics) Q. 1.359

I E Irodov Relativistic Mechanics Question 1.359

Question:

Two particles move toward each other with velocities:

• v₁ = 0.50c
• v₂ = 0.75c

relative to a laboratory frame of reference.

Find:

(a) The approach velocity of the particles in the laboratory frame.

(b) Their relative velocity.

Concepts Used in I E Irodov Q. 1.359

This problem is based on the Special Theory of Relativity.

Important concepts involved are:

• Relative velocity
• Velocity addition formula
• Laboratory frame
• Lorentz transformation
• Einstein’s velocity transformation

Students often confuse approach velocity with relative velocity. This question clearly demonstrates the difference between the two.

Easy Solution of I E Irodov Relativistic Mechanics Q. 1.359

Given:

[
v_1=0.50c
]

[
v_2=0.75c
]

The particles move towards each other.

Part (a): Approach Velocity

The approach velocity is simply the rate at which the distance between the two particles decreases in the laboratory frame.

Therefore,

[
v_{approach}=v_1+v_2
]

Substituting the values,

[
=0.50c+0.75c
]

[
=1.25c
]

Answer (a)

[
\boxed{1.25c}
]

This value can be larger than the speed of light because it is not the speed of one particle relative to the other.

It just measures the rate at which the separation between them is shrinking.

Part (b): Relative Velocity

According to Einstein’s velocity addition formula,

[
v=
\frac{v_1+v_2}
{1+\frac{v_1v_2}{c^2}}
]

Substitute the values,

# [

\frac{0.50c+0.75c}
{1+(0.50)(0.75)}
]

# [

\frac{1.25c}
{1.375}
]

[
v=0.909c
]

Answer (b)

[
\boxed{0.909c}
]

Final Answer

(a) Approach Velocity

[
\boxed{1.25c}
]

(b) Relative Velocity

[
\boxed{0.909c}
]

Simple Explanation of the Answer

Relative velocity is often thought of by many students as simply the sum of the two speeds.

This is only the case in traditional mechanics.

Special Relativity says that no object can go faster than the speed of light relative to another object.

Although the approach velocity is:

[
1.25c
]

the relative velocity becomes

[
0.909c
]

after using Einstein’s velocity addition formula.

This satisfies the principle that no relative velocity can exceed the velocity of light.

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Key Takeaways

Common Mistakes Students Should Avoid

Students commonly make these mistakes:

• Treating approach velocity as relative velocity.
• Using classical velocity addition instead of Einstein’s formula.
• Forgetting the denominator in the velocity transformation equation.
• Assuming no velocity can exceed the speed of light, even for approach speed.
• Mixing laboratory frame and particle frame.

Always identify which velocity the question is asking for before choosing the formula.

Why Practice I E Irodov Problems for JEE Advanced?

I E Irodov develops advanced problem-solving ability beyond standard JEE questions.

Benefits include:

• Strong conceptual understanding
• Better analytical thinking
• Improved application of Physics formulas
• Confidence in solving advanced numerical problems
• Better preparation for JEE Advanced and Physics Olympiads

Students should solve selected I E Irodov problems after mastering NCERT concepts and JEE Advanced-level Physics.

Is I E Irodov Q. 1.359 a JEE Main Question?

No. I E Irodov Relativistic Mechanics Q. 1.359 is not a usual JEE Main level problem.

This question is based on the theory of Special Relativity by Einstein and requires knowledge of velocity transformation, Lorentz transformation and relative motion at high speed.

It 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, then you should focus on NCERT, standard JEE level numerical problems, previous year papers and mock tests before moving to more complex 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 is a great topic to improve conceptual understanding required in JEE Advanced.

Students learn important concepts like:

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

Although only a few questions may involve relativity concepts, understanding these topics improves overall Physics problem-solving ability.

Important Topics in I E Irodov Physical Fundamentals of Mechanics

How Should Students Use I E Irodov for JEE Advanced?

The best approach is to solve I E Irodov after building strong Physics fundamentals.

Recommended preparation strategy:

Complete NCERT and school concepts

Solve JEE Main level questions

Practice JEE Advanced previous year papers

Complete coaching material

Attempt selected I E Irodov problems

Analyze mistakes and revise concepts

Students should avoid directly solving I E Irodov at the beginning of their preparation because the book is designed for advanced conceptual learning.

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 who follow AP, IB, British or any other international board should first go through the JEE syllabus and then move on to more advanced Physics 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 formulas and concepts regularly

This structured approach helps NRI students build strong conceptual understanding without unnecessary difficulty.

Related I E Irodov Relativistic Mechanics Questions

After completing Question 1.359, students can also practice:

• I E Irodov Relativistic Mechanics Q. 1.345
• I E Irodov Relativistic Mechanics Q. 1.350
• 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
• Einstein’s Velocity Addition problems
• JEE Advanced Physics previous year papers
• Mechanics revision notes
• Modern Physics practice questions
• JEE Advanced mock tests

Regular practice of advanced numerical problems helps improve analytical thinking and problem-solving speed.

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

FAQs on I E Irodov Relativistic Mechanics Q. 1.359

1. What is the main concept used in I E Irodov Q. 1.359?

The problem is based on Einstein’s velocity addition formula and relative velocity in Special Relativity.

2. Is I E Irodov Q. 1.359 useful for JEE Main?

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

3. Why is the approach velocity greater than the speed of light?

The approach velocity is simply the rate at which the distance between two particles decreases. It is not the relative velocity of one particle with respect to the other, so it can exceed the speed of light.

4. Why is the relative velocity less than the speed of light?

Einstein’s velocity addition formula ensures that the relative velocity between two particles is always less than the speed of light.

5. Is this question suitable for beginners?

No. Students should first complete Mechanics and Modern Physics 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.

Conclusion

I E Irodov Physical Fundamentals of Mechanics Relativistic Mechanics Q. 1.359 is an excellent problem for understanding the difference between approach velocity and relative velocity in Special Relativity.

The problem demonstrates that while the approach velocity may exceed the speed of light, the actual relative velocity between two particles always remains less than c, as required by Einstein’s theory of Special Relativity.

Students preparing for JEE Advanced should focus on understanding the concept behind Einstein’s velocity addition formula instead of memorizing equations. Regular practice of selected I E Irodov problems, along with JEE Advanced previous year questions, helps develop stronger analytical and problem-solving skills.