IIT JEE ADVANCED toughest question of Rotational Mechanics #jee #jeeadvanced #air1 #physics #jee2025

The Rotational Mechanics question involving two plates/discs from JEE Advanced 2016 (Paper 2) is widely regarded as one of the toughest questions in JEE history.

🌀 Question Summary

Two thin circular discs (not plates, but similar idea), rigidly connected by a massless rod.

Disc 1: Mass = m, Radius = a

Disc 2: Mass = 4m, Radius = 2a

Distance between centers =

The system rolls without slipping on a horizontal surface.

You are asked to find angular momentum about a point of contact on the ground.
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🧠 Why It’s Considered Tough

1. Multiple Rotations at Once

The system is not just rotating about its own axis — it's rolling and rotating simultaneously.

You must combine translational, rotational, and orbital motion effects.
2. Non-Uniform System

Discs have different masses and radii, which breaks symmetry.

This adds complexity in calculating the center of mass (COM) and moment of inertia.
3. Tricky Angular Momentum Calculation

You need to calculate angular momentum about a non-inertial, moving point (point of contact with the ground).

It requires using Koenig’s theorem:
4. Challenging Geometry

The distance creates a non-standard geometry.

You must calculate moments and distances with precision to find torque-free rolling.
5. Time-Consuming Algebra

Students had to carry out tedious moment of inertia calculations, especially for the spinning part about the COM and the ground.
6. Non-Standard Result

The angular velocity of the COM around the point of contact was not obvious—it turns out to be .

This non-intuitive result stumped many students.
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📉 Student Reactions

Many coaching experts and toppers called it:

“The hardest question in Rotational Mechanics ever asked in JEE.”
Even students with strong preparation found it difficult to solve in the exam time due to:

High conceptual load

Risk of calculation errors

Confusing multiple-choice options (some nearly correct)
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🔑 Skills Required

To solve it correctly, a student must:

Be strong in Rigid Body Dynamics

Understand rolling without slipping conditions deeply

Be precise with moment of inertia and angular momentum calculations

Use vector concepts and relative motion carefully
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✅ Final Verdict

Yes, the JEE Advanced 2016 Rotational Mechanics disc problem is exceptionally tough due to its blend of:

conceptual depth

tricky calculations

multi-body dynamics

and counter-intuitive results
It’s a benchmark question to test the top 1% of students.

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