IIT PHASE–2 (Advanced)
Very Tough Problems – Set 2

This set contains extreme-difficulty IIT problems where routine methods fail. These questions test energy reasoning, constraint logic, and mental stability.

Problem 1: Energy + Moving Constraint (Wedge)

Question:
A smooth wedge of mass M rests on a smooth horizontal surface. A block of mass m is released from rest at the top of the wedge. Find the speed of the block when it reaches the bottom.

Why this is tough:

• Two bodies move
• No external horizontal force
• Energy alone is insufficient

Correct strategy:

• Use conservation of energy
• Use conservation of horizontal momentum

IIT Insight: Constraint equations decide velocities.

Problem 2: Energy + Rotating Pulley

Question:
Two masses m₁ and m₂ are connected by a string over a pulley of mass M and radius R. The pulley is free to rotate. Find the speed of the system after descending height h.

Hidden difficulty:

• Rotational kinetic energy
• Moment of inertia involved

Energy accounting:

Loss in PE = KE(m₁) + KE(m₂) + Rotational KE(pulley)

Topper habit: Always check for rotational energy.

Problem 3: Energy + Elastic Limit

Question:
A block of mass m slides down a smooth incline and compresses a spring of spring constant k. Find the maximum compression.

Method:

• Gravitational PE → Spring PE
• No friction → full energy conversion

mgh = ½kx²

IIT Trap: Students unnecessarily find velocity at contact.

Problem 4: Energy + Explosion (Advanced)

Question:
A body at rest explodes into two equal parts. One part moves with speed v. Find the kinetic energy gained by the system.

Concept:

• Momentum conserved
• Energy NOT conserved

Key reasoning:

Total KE comes from internal energy.

IIT Favourite: Tests law-switching skill.

Problem 5: Energy + Potential Barrier

Question:
A particle with total energy E moves in a potential U(x) = U₀ for x > 0 and U(x) = 0 for x ≤ 0. Describe the motion classically.

Reasoning:

• If E > U₀ → motion allowed everywhere
• If E < U₀ → particle reflects

Bridge to modern physics.

Problem 6: Energy + Graph + Inequality

Question:
The potential energy of a particle varies with position as shown in a graph. Identify stable and unstable equilibrium points.

Rules:

• Stable → PE minimum
• Unstable → PE maximum

IIT Skill: Visual physics over algebra.

Problem 7: Energy + Circular Track (Extreme)

Question:
A particle moves inside a smooth vertical circular ring. Find the condition so that it never loses contact.

Advanced insight:

• Minimum speed at top matters
• Energy + force condition combined

Rank-deciding classic.

How to Practice These Problems

• Spend ≥15 minutes per problem
• Do not rush to equations
• Write energy flow in words first
• Re-solve after 2 days

“If these feel uncomfortable, you are on the right path.”