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Question #42426

Difficulty: 8/10 | 🟢 Free

The Question

A wedge with an angle of inclination $\theta$ is initially moving horizontally to the left with a constant acceleration $a$ . A block of mass $m$ is placed on the smooth inclined surface of the wedge and is attached to a light spring of spring constant $k$ . The other end of the spring is fixed to the top of the wedge. The block is initially at rest relative to the wedge. Suddenly, the acceleration of the wedge is reversed, maintaining the same magnitude $a$ but now directed to the right. Assuming the block always remains in contact with the wedge, what is the amplitude of the subsequent simple harmonic motion of the block relative to the wedge?

Options

A.
$\frac{2ma\cos\theta}{k}$
B.
$\frac{ma\cos\theta}{k}$
C.
$\frac{m(g\sin\theta + a\cos\theta)}{k}$
D.
$\frac{2m(g\sin\theta + a\cos\theta)}{k}$

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

Free Body Diagram Isolation|Effective Spring Constant|Frame of Reference Dependency

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze simple harmonic motion in a non-inertial reference frame.

The core trap lies in the shifting equilibrium position of the spring-mass system.

Students often incorrectly assume that the amplitude of oscillation is determined solely by the initial displacement from the spring's natural length, ignoring that SHM must be analyzed about the new equilibrium position where the net force is zero.

By reversing the wedge's acceleration, the pseudo-force component along the incline flips, shifting the equilibrium point.

Since the block starts at rest at the old equilibrium point, the distance between the old and new equilibrium points directly gives the correct amplitude.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Free Body Diagram Isolation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free