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Question #42469

Difficulty: 8/10 | 🟢 Free

The Question

A horizontal platform accelerates to the right with a constant acceleration $A = g$ . A wedge of mass $m$ and inclination angle $\theta = 45^\circ$ is placed on the platform and is free to slide. A small block, also of mass $m$ , is placed on the frictionless inclined surface of the wedge. All surfaces, including the contact between the wedge and the platform, are frictionless. What is the magnitude of the acceleration of the wedge relative to the platform?

Options

A.
$\frac{4}{3}g$
B.
$\frac{2}{3}g$
C.
$\frac{1}{3}g$
D.
$2g$

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

Wedge Constraint Logic|Frame of Reference Inertial vs Non-Inertial|Newton’s Second Law

Why This Question Is Tricky

Common Mistakes

Students often fail to apply the pseudo-force to both the block and the wedge when working in the non-inertial frame of the platform.

A common mistake is applying the pseudo-force only to the block to find the normal force, completely neglecting that the wedge itself is a massive body subject to the same non-inertial effects ( $MA$ ).

Furthermore, students misapply the constraint equation by assuming the block has no acceleration perpendicular to the incline in the platform frame, forgetting that the wedge's own relative acceleration $a$ gives the block a perpendicular acceleration component $a \sin\theta$ .

This question rigorously tests the simultaneous application of non-inertial dynamics and moving boundary constraints.

Quick Facts About This Question

Question Information

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