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Question #43858

Difficulty: 8/10 | 🟢 Free

The Question

A uniform thick string of mass $M$ and length $L$ is suspended from the ceiling of an elevator. A block of mass $3M$ is attached to the lower end of the string. The elevator is accelerating upwards with a constant acceleration $a = \frac{g}{3}$ , where $g$ is the acceleration due to gravity. A small transverse wave pulse is generated at the lower end of the string. What is the time taken by the wave pulse to reach the ceiling of the elevator?

Options

A.
$\sqrt{\frac{3L}{g}} (2 - \sqrt{3})$
B.
$2\sqrt{\frac{L}{g}} (2 - \sqrt{3})$
C.
$\frac{1}{2}\sqrt{\frac{L}{g}}$
D.
$\sqrt{\frac{3L}{g}} (2 + \sqrt{3})$

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

String Tension and Wave Speed|Frame of Reference Dependency|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to synthesize wave mechanics with non-inertial frame dynamics and distributed loads.

The primary trap is the assumption of a constant wave speed $v = \sqrt{T/\mu}$ .

Students often incorrectly use the tension at the bottom (or top) as a constant value throughout the string, failing to recognize that the string's own mass creates a tension gradient $T(x)$ .

Furthermore, students who do recognize the gradient often forget to apply the pseudo-force (inertial force) due to the elevator's acceleration, incorrectly using $g$ instead of $g_{\text{eff}} = g + a$ .

By forcing the integration of a spatially dependent wave speed in an accelerating frame, the problem filters out rote memorization of standard wave formulas.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Waves - Class 11 Part 2
Concept	String Tension and Wave Speed
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free