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Question #42370

Difficulty: 8/10 | 🟢 Free

The Question

A small block of mass $m = 1 \text{ kg}$ is placed on a smooth horizontal table and connected to one end of a spring with natural length $l_0 = 1 \text{ m}$ and spring constant $k = 2 \text{ N/m}$ . The other end of the spring is fixed to a point $O$ on the table. The spring exhibits an elastic after-effect, exerting an internal non-conservative damping force $F_d = -b v_r$ where $v_r$ is the radial velocity of the block. Initially, the block is at a distance $r_0 = 4 \text{ m}$ from $O$ and is given a purely transverse velocity $v_0 = 1 \text{ m/s}$ . Due to the damping force, the radial motion eventually ceases, and the block settles into a steady circular orbit around $O$ . Find the total work done by the non-conservative damping force during this entire process.

Options

A.
$-6.5 \text{ J}$
B.
$-4.5 \text{ J}$
C.
$0 \text{ J}$
D.
$-8.0 \text{ J}$

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

Angular Momentum conservation|Conservative vs Non-conservative|Variable Force Integration

Why This Question Is Tricky

Common Mistakes

Students incorrectly assume that if a system is isolated from external torques (conserving angular momentum), it must also conserve mechanical energy, especially when the primary force is conservative (a spring).

The trap exploits the conditioning to equate L-conservation with E-conservation.

The presence of an internal velocity-dependent damping force breaks mechanical energy conservation without violating angular momentum conservation, because the damping force is purely radial (cross product of position vector and damping force is zero).

The problem tests the ability to decouple these conservation laws and correctly apply the work-energy theorem to a system with internal dissipation.

Quick Facts About This Question

Question Information

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