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Question #42365

Difficulty: 8/10 | 🟢 Free

The Question

A uniform rod of mass $m$ and length $l$ is suspended vertically from a hinge $A$ . The hinge is attached to a block of mass $M = 2m$ which can slide without friction along a horizontal overhead rail. Initially, the system is at rest. A horizontal impulse $J$ is applied to the bottom end $B$ of the rod. Find the angular velocity $\omega$ of the rod immediately after the impulse.

Options

A.
$\frac{10J}{3ml}$
B.
$\frac{3J}{ml}$
C.
$\frac{6J}{ml}$
D.
$\frac{9J}{2ml}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Torque about non-fixed axes|Rigid Body Constraints|Impulse-Momentum Theorem

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Impulse-Momentum Theorem on a system with a non-fixed axis of rotation.

A common trap is for students to visually identify the hinge $A$ as the instantaneous axis of rotation (IAR) and incorrectly apply $L = I\omega$ about it ( $Jl = \frac{1}{3}ml^2\omega$ ), yielding the trap answer $3J/ml$ .

They fail to account for the fact that the hinge itself experiences a sudden change in velocity (acceleration) due to the constraint impulse, meaning it is not a valid inertial frame for the simple $L=I\omega$ relation.

The robust approach requires applying linear impulse to the system and angular impulse about the rod's COM, explicitly accounting for the constraint impulse between the block and the rod.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Torque about non-fixed axes
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free