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Question #42047

Difficulty: 8/10 | 🟢 Free

The Question

A block of mass $m$ is placed on the inclined surface of a rough wedge of angle $\theta = 37^\circ$ . The wedge accelerates horizontally to the right with a time-varying acceleration $a(t) = 5t \text{ m/s}^2$ (where $t$ is in seconds). The wedge is oriented such that its inclined surface faces the right (i.e., the block slides down the incline towards the right). The coefficient of friction between the block and the wedge is $\mu = 0.5$ . If the block is released from rest relative to the wedge at $t = 0$ , at what time $t > 0$ does the block momentarily come to rest relative to the wedge? (Take $g = 10 \text{ m/s}^2$ , $\sin 37^\circ = 3/5$ , $\cos 37^\circ = 4/5$ )

Options

A.
$\frac{8}{11} \text{ s}$
B.
$1 \text{ s}$
C.
$\frac{8}{5} \text{ s}$
D.
$\frac{8}{3} \text{ s}$

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

Relative Velocity in 1D|Normal Force at Angles|Power-Velocity Relationship

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to construct a Free Body Diagram in a non-inertial reference frame with a time-varying acceleration.

The primary trap lies in the assumption that the normal force remains constant ( $N = mg \cos\theta$ ), which leads to an incorrect constant friction force.

By making the wedge's acceleration time-dependent, the pseudo force introduces a time-varying component to both the normal force and the driving force along the incline.

Students who rely on memorized formulas for inclined planes will fail to account for the fictitious force's perpendicular component, missing the time-dependent nature of the kinetic friction and resulting in an incorrect integration for the relative velocity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Relative Velocity in 1D
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free