A heavy uniform chain lies on a horizontal table top. If the...

A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$ then the maximum fraction of length of the chain, that can hang over one edge of the table is
(a) $20 \%$
(b) $25 \%$
(c) $35 \%$
(d) 1576

Key Concepts

Static Friction

Static friction is the resistive force that prevents relative motion between surfaces in contact. It is proportional to the normal reaction force and is characterized by the coefficient of static friction. In problems involving objects at rest, such as a chain on a table, static friction determines how much force can be applied before motion begins, making it critical for analyzing conditions of impending motion or equilibrium.

Center of Mass

The center of mass of an object is the point where the entire mass of a system can be considered to be concentrated for the purpose of analysis of translational motion. For a uniform chain, the center of mass lies at its geometric center. In equilibrium problems, knowing the location of the center of mass helps in calculating the net gravitational force and the resulting torque, especially when part of the object is suspended or overhanging.

Static Equilibrium

Static equilibrium refers to the state of a system where all forces and torques are balanced, resulting in no net motion. In analyzing problems like a chain partially overhanging a table, the conditions for static equilibrium involve balancing the gravitational force on the overhanging segment with the frictional force on the segment resting on the table. This analysis ensures that the system is at the threshold of motion, allowing one to compute the maximum permissible overhang.

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