In the given arrangement, n number of equal masses are...

In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to $n^{\text {th }}$ mass is :
(a) $\frac{m M g}{n m+M}$
(b) $\frac{m M g}{n m M}$
(c) $m g$
(d) $\mathrm{mng}$

Key Concepts

Multiple Mass Systems

When dealing with systems composed of several masses connected in series, it is important to recognize that different segments of the connecting material (such as strings) may experience different tensions. This is because each segment must support not only the mass directly attached to it, but also the cumulative weight of all the masses below that point in the system.

Gravitational Force (Weight)

Weight is the force exerted on a mass by gravity, calculated as the product of the mass and the gravitational acceleration (mg). In problems involving vertical arrangements of masses, this force plays a critical role in determining the tension in the strings, as each segment must counteract the weight of the masses it supports.

Free-Body Diagram Analysis

A free-body diagram is a schematic representation of an object isolated from its surroundings, showing all the external forces acting upon it. This tool is essential in mechanics for systematically analyzing forces like tension and weight, helping to apply Newton's laws accurately to individual components of a system.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is fundamental for analyzing the forces in any mechanical system, including those involving masses and strings, as it provides the relationship needed to determine unknown forces such as tension.

Tension in Massless Strings

In systems where the strings have negligible mass, the tension is transmitted uniformly along the length of the string, assuming no acceleration or that the system is in equilibrium. This concept is crucial because it simplifies the analysis by allowing us to treat the string as a conduit for force without any additional weight or inertia affecting the tension distribution.

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