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Question #42458

Difficulty: 8/10 | 🟢 Free

The Question

A uniform rigid rod of mass $m$ and length $L$ is initially at rest on a smooth horizontal surface. An impulsive force of magnitude $J$ is applied at one end of the rod. The direction of the impulse makes an angle $\theta = \frac{\pi}{6}$ with the longitudinal axis of the rod. What is the distance of the instantaneous center of rotation (ICR) of the rod from its center of mass immediately after the impulse?

Options

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

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

Impulse-Momentum Theorem|Collision Impulses|Rigid Body Constraints|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of the Impulse-Momentum theorem and rigid body kinematics.

A common trap is ignoring the longitudinal component of the impulse, assuming it does not contribute to rotation and thus incorrectly discarding the longitudinal velocity of the CoM.

This leads to the incorrect ICR distance of L/6.

Students must enforce the full 2D vector constraint $\vec{v}_{ICR} = \vec{v}_c + \vec{\omega} \times \vec{r}_{ICR} = 0$ , recognizing that the ICR lies off the rod's axis when the impulse is not perfectly perpendicular.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Impulse-Momentum Theorem
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free