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

A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of the length of the chain that can hang over one edge of the table is (a) $20 \%$ (b) $25 \%_{6}$ (c) $35 \%$ (d) $15^{\circ 6}$

A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of the length of the chain that can hang over one edge of the table is
(a) $20 \%$
(b) $25 \%_{6}$
(c) $35 \%$
(d) $15^{\circ 6}$

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Key Concepts

Static Equilibrium

Static equilibrium is the state in which an object remains at rest because the net force and net torque acting on it are zero. This concept is essential for analyzing conditions under which forces, such as weight and friction, balance each other, ensuring that the system does not move.

Friction

Friction is the resistive force that opposes movement between two contacting surfaces. Specifically, static friction, which is proportional to the normal force through a coefficient, prevents the initiation of motion until its maximum limit is surpassed, playing a crucial role in equilibrium analyses.

Uniform Distribution of Mass

A uniform distribution of mass in an extended object means that the mass is spread evenly along its length. This concept simplifies analysis by allowing one to locate the center of mass at the geometric center, which is key in evaluating how weight is distributed and how it influences equilibrium.

Force Analysis in Continuous Systems

In continuous systems, objects are analyzed by considering how forces are distributed along their length or volume. This involves breaking the object into segments to calculate contributions from different parts, enabling a detailed balance of competing forces such as gravitational pull and frictional resistance.

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