STAGE–5 : ADDITIONAL MATERIAL – PART–3 (CONTINUATION)

IIT PYQs as Proofs – Mixed Systems, Contradictions & Option Elimination

🔷 12. PYQ–7 (MIXED SYSTEM): BLOCK + INCLINE + PULLEY

Problem (IIT–JEE):
A block of mass m₁ rests on a rough inclined plane of angle θ. It is connected by a light string over a smooth pulley to a hanging mass m₂. Coefficient of friction between block and plane is μ. Find the condition for motion and acceleration.

🔹 Proof Strategy (NOT Calculation First)

Before writing equations, IIT expects you to ask:

Which block has greater tendency to move?
What resists that tendency?
Is motion even possible?

Key Insight:
Motion depends on comparison of driving force and limiting friction.

🔹 Driving vs Resisting Forces

Driving force (if m₂ moves down):

Driving = m₂g − m₁g sinθ

Maximum resisting force on m₁:

Resisting = μm₁g cosθ

🔹 Proof of Motion Condition

Motion occurs only if:

m₂g − m₁g sinθ > μm₁g cosθ

If this inequality fails, no motion is possible — regardless of equations.

This is not a formula. This is a logical necessity.

🔷 13. PYQ–8: WHY SYSTEM APPROACH FAILS IN SOME FRICTION PROBLEMS

Problem Pattern:
Two blocks connected, one on rough surface, one smooth.

🔹 Common Student Mistake

Students take both blocks as a single system.

Why this fails:
Friction is different for different blocks.

🔹 Proof Logic

System approach cancels internal forces only if:

Acceleration is same
External forces act uniformly

When friction differs:

External forces differ
Optimization must be done block-wise

IIT Rule:
Use system approach only when external force distribution is uniform.

🔷 14. PYQ–9: “WHICH OPTION MUST BE CORRECT?” (ELIMINATION PROOF)

Problem Type:
Four options given for acceleration. Numerical solving is lengthy.

🔹 IIT Elimination Proof

Check extreme cases:

μ → 0 (frictionless)
θ → 0 (horizontal)
m₂ → 0 (no hanging mass)

Any option that fails even one extreme is automatically wrong.

Rank Logic:
Correct answer must work for all physical limits.

🔷 15. PYQ–10: CONTRADICTION METHOD (VERY RARE BUT POWERFUL)

Problem:
Assume the block moves upward. Show contradiction.

🔹 Proof Method

Assume upward motion. Then friction must act downward.

Write force balance. If acceleration comes negative → assumption false.

Conclusion:
Actual motion must be opposite.

IIT frequently hides this logic inside conceptual MCQs.

🔷 16. WHY IIT ANSWERS LOOK “SIMPLE” AFTER SOLUTION

Because:

Unnecessary variables cancel
Constraints dominate behavior
Physics limits reduce complexity

Complex appearance ≠ complex physics.

🔷 17. PYQ META-PATTERN (VERY IMPORTANT)

From 20+ years of PYQs:

70% questions → threshold or limit based
20% → mixed systems
10% → pure conceptual traps

IIT tests control, not speed.

🔷 18. HOW TO PRACTICE PYQs AT STAGE–5 LEVEL

Hide the solution
Predict answer direction
Check limiting cases
Only then calculate
Finally, explain why other options fail

If you can explain why three options are wrong, you don’t need to fear the correct one.

🔷 19. TRANSITION TO PART–4

Part–4 will be the killer section:

Complete mixed-system PYQs (full derivations)
Optimization under time pressure
Rank-level shortcuts (with proof, no cheating)
JEE Main vs Advanced execution differences

✅ STAGE–5 – ADDITIONAL MATERIAL (PART–3 COMPLETE – A + B)

MIND GROW Magazine