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Question #42448

Difficulty: 8/10 | 🟢 Free

The Question

A wedge of mass $M = 3 \text{ kg}$ and inclination angle $\theta = 45^\circ$ is placed on a smooth horizontal surface. A block of mass $m = 2 \text{ kg}$ is placed on the smooth inclined surface of the wedge. The system is released from rest. Taking the acceleration due to gravity as $g = 10 \text{ m/s}^2$ , what is the magnitude of the normal force exerted by the wedge on the block during the motion?

Options

A.
$\frac{15\sqrt{2}}{2} \text{ N}$
B.
$10\sqrt{2} \text{ N}$
C.
$15\sqrt{2} \text{ N}$
D.
$\frac{25\sqrt{2}}{2} \text{ N}$

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

Newton’s Third Law Pairing|Wedge Constraint Logic|System vs Particle Displacement

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly apply Newton's Second Law in a non-inertial reference frame, specifically focusing on acceleration coupling via a wedge constraint.

The lethal trap is assuming the normal force is simply the static component of gravity ( $N = mg \cos \theta$ ), which ignores the recoil acceleration of the wedge.

Students must recognize that the wedge's acceleration introduces a pseudo force in its frame, modifying the force balance perpendicular to the incline to $N = m(g \cos \theta - a \sin \theta)$ .

Failing to couple the equations of motion of both bodies leads directly to the incorrect static normal force option.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Newton’s Third Law Pairing
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free