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Question #42382

Difficulty: 8/10 | 🟢 Free

The Question

A truck accelerates horizontally to the right with a constant acceleration $a = \frac{g}{2}$ . Inside the truck, a fixed inclined plane makes an angle $\theta = 45^\circ$ with the horizontal floor. The incline slopes downward to the right (i.e., in the direction of the truck's acceleration). A solid sphere of mass $m$ and radius $R$ is released from rest on the incline. What is the minimum coefficient of static friction $\mu$ between the sphere and the incline required for the sphere to undergo pure rolling?

Options

A.
$\frac{2}{21}$
B.
$\frac{2}{7}$
C.
$\frac{6}{7}$
D.
$\frac{2}{15}$

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

Rolling on Inclines|Accelerated Frame Hydrostatics|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze rolling motion in an accelerated non-inertial reference frame.

The primary trap is failing to account for the pseudo force's effect on both the normal force and the driving force down the incline.

Students often mistakenly use the standard pure rolling condition $\mu \ge \frac{2}{7}\tan\theta$ (yielding $2/7$ ), ignoring that the effective gravity vector has rotated.

Another common error is applying the pseudo force with the incorrect sign, which would lead to adding the components instead of subtracting them for the driving force, yielding the trap answer $6/7$ .

By transforming to the truck's frame, the problem elegantly reduces to standard rolling on an incline with a modified effective angle $\alpha$ , where $\tan\alpha = \frac{g\sin\theta - a\cos\theta}{g\cos\theta + a\sin\theta}$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Rolling on Inclines
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free