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Question #42494

Difficulty: 8/10 | 🟢 Free

The Question

A uniform rod of mass $M$ and length $L$ is at rest on a smooth horizontal surface. A small particle of mass $m = \frac{M}{2}$ moving with a velocity $v_0$ perpendicular to the length of the rod strikes one of its ends and sticks to it. What is the angular velocity of the resulting system immediately after the collision?

Options

A.
$\frac{v_0}{L}$
B.
$\frac{6v_0}{5L}$
C.
$\frac{3v_0}{2L}$
D.
$\frac{2v_0}{L}$

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

Collision Impulses|Torque about non-fixed axes|Vector Cross-Product

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly apply the conservation of angular momentum in a system where the axis of rotation shifts post-collision.

A common trap is calculating the initial angular momentum about the rod's original center of mass ( $L_i = Mv_0L/4$ ) and equating it to the final angular momentum about either the old or new center of mass.

Students must recognize that for a non-pivoted rigid body, post-collision rotation occurs strictly about the new center of mass, and angular momentum must be conserved about this specific moving point to avoid pseudo-torque complications.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Collision Impulses
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free