I E Irodov Physical Fundamentals Of Mechanics (Relativistic Mechanics) Q. 1.345

I E Irodov Physical Fundamentals of Mechanics is one of the best Physics book among the students preparing for JEE Advanced and other competitive exams. The book contains advanced conceptual problems to help students to improve their ability in solving Physics problems.

The chapter Relativistic Mechanics covers topics that are related to special relativity, motion at very high speeds, dilation of time, and length contraction.

This page contains step by step solution of I E Irodov Physical Fundamentals of Mechanics (Relativistic Mechanics) Question 1.345 along with concepts required for JEE Advanced preparation.

I E Irodov Relativistic Mechanics Question 1.345

Question:

A rod flies with constant velocity past a mark which is stationary in reference frame K.

In frame K, it takes:

Δt = 20 ns

for the rod to fly past the mark.

In the reference frame fixed to the rod, the mark moves past the rod for:

Δt’ = 25 ns

Find the proper length of the rod.

Concepts Used in I E Irodov Q.1.345

This problem is based on the Special Theory of Relativity.

Important concepts used:

• Length contraction
• Time dilation
• Relative motion
• Proper length
• Lorentz factor

Understanding these concepts helps students solve advanced mechanics problems for JEE Advanced.

Easy Solution of I E Irodov Relativistic Mechanics Q.1.345

Given:

Time measured in reference frame K:

Δt = 20 ns

Time measured in the rod reference frame:

Δt’ = 25 ns

Let:

v = velocity of rod

L = length observed from frame K

L₀ = proper length of rod

The proper length is the actual length measured when the object is at rest.

Step 1: Length Observed in Frame K

In frame K, the rod is moving.

Therefore:

L = vΔt

Putting value:

L = v × 20 ns

Step 2: Length in Rod Frame

In the rod’s own reference frame, the rod is stationary.

Therefore:

L₀ = vΔt’

Putting value:

L₀ = v × 25 ns

Step 3: Apply Length Contraction Formula

According to special relativity:

L = L₀√(1-v²/c²)

Now,

L/L₀ = 20/25

L/L₀ = 0.8

Therefore:

0.8 = √(1-v²/c²)

Squaring both sides:

0.64 = 1-v²/c²

v²/c² = 0.36

v/c = 0.6

Therefore:

v = 0.6c

Step 4: Find Proper Length of Rod

Formula:

L₀ = vΔt’

Now:

v = 0.6c

Speed of light:

c = 3 × 10⁸ m/s

Time:

Δt’ = 25 × 10⁻⁹ s

Putting values:

L₀ = 0.6 × 3 × 10⁸ × 25 × 10⁻⁹

L₀ = 4.5 m

Final Answer

The proper length of the rod is:

L₀ = 4.5 metres

Simple Explanation of Answer

The rod is moving at a speed close to the speed of light so an observer sees the rod length contracted.

In the rod frame the rod is at rest and the true length is measured.

The difference of both observed times allows us to find the velocity of the rod and to calculate its proper length.

The actual length of the rod is 4.5 m.

Common Mistakes Students Make in I E Irodov Q.1.345

• Confusing proper length with the contracted length measured in frame K.
• Using 20 ns instead of 25 ns while calculating the proper length.
• Forgetting that the rod is at rest in its own reference frame.
• Applying the time dilation formula without first identifying the correct reference frame.
• Using the speed of light without converting nanoseconds into seconds.

Why Practice I E Irodov Problems for JEE Advanced?

I E Irodov problems are useful because they improve deep Physics understanding.

Benefits:

• Builds strong concepts
• Improves analytical thinking
• Develops problem-solving skills
• Helps in advanced numerical practice
• Improves JEE Advanced preparation

Students aiming for top IITs can practice selected I E Irodov questions after completing basic JEE concepts.

Is I E Irodov Required for JEE Main?

I E Irodov is not mandatory for JEE Main preparation.

For JEE Main, students should focus on:

• NCERT concepts
• JEE syllabus
• Previous year questions
• Mock tests

I E Irodov is more useful for students preparing for difficult JEE Advanced Physics problems.

Important Topics in I E Irodov Physical Fundamentals of Mechanics

The Mechanics section includes:

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How Should Students Prepare I E Irodov for JEE Advanced?

Recommended preparation order:

This method helps students use I E Irodov effectively.

I E Irodov for NRI JEE Students

NRI students preparing for JEE from the USA, UAE, Saudi Arabia, Qatar, Oman, Kuwait and Bahrain can use selected I E Irodov problems for advanced Physics preparation.

Students preparing online for IIT JEE should first complete JEE concepts and then move towards advanced reference books like I E Irodov.

Related I E Irodov Relativistic Mechanics Questions

Students can continue practicing the following I E Irodov Relativistic Mechanics questions after completing Q.1.345:

• I E Irodov Relativistic Mechanics Q.1.350
• I E Irodov Relativistic Mechanics Q.1.359
• I E Irodov Relativistic Mechanics Q.1.378
• I E Irodov Relativistic Mechanics Q.1.388

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

FAQs on I E Irodov Relativistic Mechanics Q.1.345

1. Is I E Irodov Q.1.345 important for JEE Advanced?

Yes. It helps students understand advanced relativity concepts useful for Physics problem solving.

2. Which concept is used in I E Irodov Q.1.345?

This question uses length contraction, time relation and special relativity concepts.

3. Is I E Irodov useful for JEE Main?

I E Irodov is generally above JEE Main level. It is mainly useful for JEE Advanced preparation.

4. What is the answer of I E Irodov Relativistic Mechanics Q.1.345?

The proper length of the rod is:

4.5 metres.