Before You Begin

Question #42358

Difficulty: 8/10 | 🟢 Free

The Question

Two blocks, A and B, of masses $2m$ and $m$ respectively, are connected by a massless spring of spring constant $k$ . They are placed on a horizontal surface such that block A is on a rough patch with a coefficient of kinetic friction $\mu$ , while block B is on a smooth patch. Initially, the spring is at its natural length and the entire system is given an initial velocity $v_0$ in the direction from A to B. Assuming $v_0$ is sufficiently large so that block A does not stop before the spring reaches its maximum extension, what is the maximum extension of the spring?

Options

A.
$\frac{4\mu mg}{3k}$
B.
$\frac{4\mu mg}{k}$
C.
$\frac{2\mu mg}{3k}$
D.
$\frac{2\mu mg}{k}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

System vs Particle Displacement|Kinetic Friction Transition|Integration

Why This Question Is Tricky

Common Mistakes

This question targets a notorious misconception regarding the Work-Energy Theorem for deformable systems.

Students frequently conflate the work done by friction ( $W = \int \vec{f} \cdot d\vec{r}_{contact}$ ) with the macroscopic pseudo-work ( $\int \vec{F}_{net} \cdot d\vec{r}_{cm}$ ).

Because friction acts asymmetrically on the system, the actual energy dissipated depends on the internal relative displacement, not just the CM displacement.

By shifting to the CM frame and incorporating pseudo forces, the problem elegantly isolates the internal energy balance, trapping students who blindly apply $-f_{net} x_{cm} = \Delta K + \Delta U$ or who incorrectly use the total friction force to calculate relative work.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	System vs Particle Displacement
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free