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Question #42421

Difficulty: 8/10 | 🟢 Free

The Question

A wedge of mass $M = 3m$ with an inclination angle $\theta = 30^\circ$ rests on a smooth horizontal surface. The inclined surface faces left (elevation increases to the right). A thin hollow spherical shell of mass $m$ and radius $R$ is placed on the incline. A horizontal force $F$ is applied to the wedge to the left. Assuming the shell rolls without slipping on the wedge, what is the acceleration of the wedge $a_w$ ?

Options

A.
$\frac{20F - 3\sqrt{3} mg}{71 m}$
B.
$\frac{4F - \sqrt{3} mg}{13 m}$
C.
$\frac{6F - \sqrt{3} mg}{21 m}$
D.
$\frac{20F - 3\sqrt{3} mg}{66 m}$

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

Frame of Reference Inertial vs Non-Inertial|Rolling on Inclines|Integration

Why This Question Is Tricky

Common Mistakes

This problem tests the rigorous application of Newton's laws and pure rolling constraints within a non-inertial reference frame.

The primary trap is failing to account for the pseudo-force's perpendicular component, which alters the normal force ( $N = mg\cos\theta + ma_w\sin\theta$ ) and consequently the horizontal force transmitted to the wedge.

Additionally, students frequently misapply the rolling constraint by either using the incorrect moment of inertia for a hollow sphere or failing to correctly couple the dynamically adjusting static friction force with the tilted effective gravity vector in the coupled system equations.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Frame of Reference Inertial vs Non-Inertial
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free