Before You Begin

Question #42495

Difficulty: 8/10 | 🟢 Free

The Question

A uniform rod of mass $M = 2 \text{ kg}$ and length $L = 1 \text{ m}$ is pivoted at its upper end $O$ and hangs vertically at rest. A point particle of mass $m = 1 \text{ kg}$ moving horizontally with a velocity $v_0 = 10 \text{ m/s}$ strikes the lower end of the rod and sticks to it. The pivot $O$ exerts a constant non-conservative frictional torque $\tau_f = \frac{60}{\pi} \text{ N m}$ opposing the rotation. Assuming the acceleration due to gravity is $g = 10 \text{ m/s}^2$ , what is the maximum angular displacement $\theta$ (in radians) of the rod before it momentarily comes to rest?

Options

A.
$\frac{\pi}{3}$
B.
$\frac{\pi}{2}$
C.
$\frac{2\pi}{3}$
D.
$\frac{\pi}{4}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Collision Impulses|Work-Energy Theorem for Rotation|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the correct application of the Work-Energy Theorem in a system involving both a perfectly inelastic collision and a path-dependent non-conservative force (frictional torque).

The primary trap is conflating the initial kinetic energy of the particle with the kinetic energy of the system post-collision.

Students who incorrectly apply energy conservation from the very beginning (ignoring the energy lost during the inelastic impact) will set the initial energy to $50 \text{ J}$ and arrive at the trap answer $\pi/2$ .

Another trap is ignoring the non-conservative work done by friction entirely, which leads to $2\pi/3$ .

The problem enforces the strict separation of the impulsive phase (where only angular momentum is conserved) and the subsequent rotational phase (where the Work-Energy Theorem accounts for both conservative and non-conservative work).

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