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Question #42612

Difficulty: 8/10 | 🟢 Free

The Question

A fixed point mass $M$ is located at the origin $O$ . A smooth rigid circular wire of radius $R$ is fixed in a plane containing $O$ , such that its center $C$ is at a distance $2R$ from $O$ . A small bead of mass $m$ is released from rest at the point on the wire farthest from $O$ . When it reaches the point on the wire closest to $O$ , it undergoes a perfectly inelastic collision with another stationary bead of mass $m$ . Find the magnitude of the normal force exerted by the wire on the combined mass immediately after the collision. (Assume $G$ is the universal gravitational constant)

Options

A.
$\frac{8GMm}{3R^2}$
B.
$\frac{4GMm}{R^2}$
C.
$\frac{2GMm}{3R^2}$
D.
$\frac{5GMm}{3R^2}$

Check Your Answer

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

Energy Partitioning|Vertical Circular Motion|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze circular motion in a non-uniform, central gravitational field, bypassing the standard $mgh$ approximation.

The primary trap lies in incorrectly assuming a uniform gravitational field $g = GM/R^2$ over the path, which leads to an erroneous velocity before collision.

Additionally, students often forget that the centripetal equation requires the vector sum of the normal force and the local gravitational force; neglecting the gravitational pull of the central mass $M$ on the combined mass $2m$ during the radial force balance yields a severely underestimated normal force.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Oscillations - Class 11 Part 2
Concept	Energy Partitioning
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free