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Question #42209

Difficulty: 8/10 | 🟢 Free

The Question

A small block of mass $m = 1 \text{ kg}$ is attached to one end of a light elastic string of natural length $L_0 = 1 \text{ m}$ and stiffness $k = 12 \text{ N/m}$ . The other end of the string is fixed to a point on a smooth horizontal table. The block is initially revolving in a horizontal circle with an angular velocity $\omega_1 = 2 \text{ rad/s}$ . An external mechanism slowly increases the angular velocity of the block to $\omega_2 = 3 \text{ rad/s}$ . Calculate the work done by the external mechanism during this process.

Options

A.
$120 \text{ J}$
B.
$67.5 \text{ J}$
C.
$2.5 \text{ J}$
D.
$126 \text{ J}$

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

Work Done in Stretching|System vs Particle Displacement|Center of Mass (COM) Frame

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to recognize that the moment of inertia of a system with an elastic constraint is dynamically coupled to its angular velocity.

A common trap is assuming the radius remains constant at $L_0$ , leading to a simple kinetic energy difference calculation.

Another lethal mistake is calculating the new radii correctly but forgetting to include the elastic potential energy stored in the stretched string when applying the work-energy theorem.

The correct approach requires balancing the centripetal force with the spring force to find the variable radius, and then calculating the change in total mechanical energy (both kinetic and elastic potential).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Solids - Class 11 Part 2
Concept	Work Done in Stretching
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free