Rotational Motion – Tough Objective Questions (Page 7)

Multi-Concept • Rank-Deciding • IIT-JEE Advanced Level

This page contains very tough objective questions involving energy + angular momentum + friction + constraints. These questions separate top 1% from the rest.

Q1. (IIT-JEE Advanced)

A uniform rod of length L is hinged at one end and released from rest in horizontal position. What is the angular speed when it becomes vertical?

Method:

Use energy conservation (hinge does no work).

Loss in PE = gain in rotational KE

mg(L/2) = ½ Iω²
I = (1/3)mL²

ω = √(3g/L)

Answer: ω = √(3g/L)

Examiner Trap: Many students use linear KE wrongly.

Q2. (JEE Advanced)

A disc rolls without slipping on a rough surface. Which statement is correct?

A) Friction does positive work
B) Friction does negative work
C) Friction does zero work
D) Friction changes mechanical energy

Key Idea:

In pure rolling, point of contact has zero displacement.

Answer: C) Friction does zero work

Trap: Students assume friction always dissipates energy.

Q3. (IIT-JEE Advanced)

A disc and a ring of same mass and radius roll down an incline. Ratio of their linear accelerations is:

Method:

a = g sinθ / (1 + I/MR²)

Disc: I/MR² = 1/2
Ring: I/MR² = 1

Answer: a_disc : a_ring = 4 : 3

Q4. (IIT-JEE)

A rotating body has constant angular momentum. Which quantity must remain constant?

A) Angular speed
B) Moment of inertia
C) Rotational KE
D) None

Thinking:

L = Iω → product constant, not individual terms.

Answer: D) None

Trap: Confusing conservation with constancy.

Q5. (JEE Advanced – Assertion Type)

Assertion: A particle moving in a straight line can have angular momentum.
Reason: Angular momentum depends on reference point.

Correct Logic:

Angular momentum L = r × p

Answer: Both true and reason explains assertion

Q6. (IIT-JEE Advanced)

A disc slides on a rough surface and gradually starts rolling. Which statement is correct?

Concept:

Friction reduces translational speed but increases angular speed.

Answer: Translational KE decreases, rotational KE increases initially

Q7. (JEE Advanced)

A body rotating with angular speed ω has angular momentum zero. Which is possible?

Key Idea:

Angular momentum depends on chosen axis.

Answer: Axis passing through centre of mass

TOPPER STRATEGY FOR PAGE-7 QUESTIONS

✔ Identify conserved quantity first
✔ Decide axis before calculations
✔ Use I/MR² table mentally
✔ Energy only if no non-conservative work
✔ For rolling: write translation + rotation separately

WHY THESE QUESTIONS ARE DANGEROUS

❌ Hidden assumptions
❌ Mixed linear + rotational ideas
❌ Reference-point dependence
❌ Energy vs momentum confusion

Next: Page 8 – Ultra-Extreme Objective Questions (Top 500 Rank Level)

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