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 nth mass is
(a) $\frac{\mathrm{mHlg}}{n m+M}$
(b) $\frac{m M g}{n m M}$
(c) $m g$
(d) mhg

Key Concepts

Tension in Strings

Tension is the force transmitted through a string, rope, or similar object when forces are applied at both ends. In systems with multiple masses connected by strings, the tension in each segment can vary depending on the forces acting on the masses below that segment. Understanding tension involves recognizing how the weight of the masses and any additional forces (such as acceleration) contribute to the overall force experienced by the string.

Free-Body Analysis

Free-body analysis is a fundamental technique in mechanics used to isolate a single object or component within a system to identify all the forces acting on it. By drawing a free-body diagram for the mass connected by the string, one can determine the net force and hence the tension required to maintain equilibrium or cause acceleration, depending on the problem scenario.

Static Equilibrium and Newton’s Laws

In many arrangements of connected masses, analyzing static equilibrium (where the net force acting on each mass is zero) is essential. Newton's laws, particularly the first and second laws, provide the mathematical framework to relate the forces acting on a mass (including gravitational force) to the resulting tension in the connecting strings. When a mass is at rest or moving at constant velocity, the tension in the string connected to it typically equals the weight of the mass it supports.

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