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Question #43507

Difficulty: 8/10 | 🟢 Free

The Question

A solid sphere of mass $m$ and radius $R$ is initially at rest on a wedge of mass $M$ and inclination angle $\theta$ . The wedge rests on a smooth horizontal surface. A horizontal impulse of magnitude $J$ is applied to the wedge. Assuming the coefficient of friction between the sphere and the wedge is sufficient to ensure pure rolling of the sphere on the wedge during and after the impulse, find the initial angular velocity $\omega_0$ of the sphere immediately after the impulse.

Options

A.
$\frac{5 J \cos\theta}{R [7M + m(7 - 5\cos^2\theta)]}$
B.
$\frac{5 J \cos\theta}{7 R (M + m)}$
C.
$\frac{5 J \cos\theta}{R [7M + m(7 + 5\cos^2\theta)]}$
D.
$\frac{7 J \cos\theta}{R [5M + m(5 - 7\cos^2\theta)]}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Frame of Reference|Pure Rolling Condition|System of Particles and Rotational Motion

Why This Question Is Tricky

Common Mistakes

This question tests the ability to analyze impulsive motion in non-inertial reference frames.

A common trap is applying conservation of angular momentum about the contact point in the ground frame without accounting for the acceleration of that point, or shifting to the wedge frame but neglecting the impulsive pseudo-torque acting on the sphere's center of mass.

Furthermore, students often incorrectly assume the sphere's absolute horizontal velocity is simply equal to the wedge's velocity, failing to subtract the horizontal component of the relative rolling velocity when applying the system's horizontal impulse-momentum theorem.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Frame of Reference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free