Before You Begin

Question #42028

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m = 1 \text{ kg}$ is projected from the origin $x=0$ along the positive x-axis with an initial speed $v_0 = 20 \text{ m/s}$ on a smooth horizontal surface. The particle moves through a resistive medium that exerts a drag force of magnitude $F_d = kS$ , where $k = 4 \text{ N/m}$ and $S$ is the total path length covered by the particle from the start of its motion. The force always acts opposite to the velocity vector. At $x = L = 2 \text{ m}$ , the particle undergoes a head-on inelastic collision with a fixed vertical wall. If the coefficient of restitution is $e = 0.5$ , what is the kinetic energy of the particle just as it returns to the origin $x=0$ ?

Options

A.
$24 \text{ J}$
B.
$40 \text{ J}$
C.
$48 \text{ J}$
D.
$56 \text{ J}$

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

Displacement vs. Total Path Length|Coefficient of Restitution|Work against Conservative Force|Calculus Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between displacement-dependent conservative forces (like a spring, $F = -kx$ ) and path-length-dependent non-conservative forces (like cumulative drag, $F = -kS$ ).

A common trap is assuming the energy loss during the return trip is identical to the outward trip (yielding $40 \text{ J}$ ) or treating the force as conservative (yielding $56 \text{ J}$ ).

Furthermore, it rigorously tests the application of the Work-Energy Theorem over an integro-differential path rather than relying on simple $F=ma$ kinematics, coupled with the correct scalar scaling of kinetic energy ( $e^2$ ) during an inelastic collision.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Displacement vs. Total Path Length
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free