A light spring balance hangs from the hook of the other...

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M \mathrm{~kg}$ hangs from the former one. Then the true statement about the scale reading is (A) Both the scales read $M \mathrm{~kg}$ each (B) The scale of the lower one reads $M \mathrm{~kg}$ and of the upper one zero (C) The reading of the two scales can be anything but the sum of the readings will be $M \mathrm{~kg}$ (D) Both the scales read $M / 2 \mathrm{~kg}$

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M \mathrm{~kg}$ hangs from the former one. Then the true statement about the scale reading is
(A) Both the scales read $M \mathrm{~kg}$ each
(B) The scale of the lower one reads $M \mathrm{~kg}$ and of the upper one zero
(C) The reading of the two scales can be anything but the sum of the readings will be $M \mathrm{~kg}$
(D) Both the scales read $M / 2 \mathrm{~kg}$

Key Concepts

Equilibrium in Static Systems

This concept deals with the principle that when a system is at rest, all forces acting on it must balance out. In the context of the problem, the block hanging from the spring balances is in equilibrium, meaning the upward forces (tensions in the spring balances) exactly balance the downward force of gravity (the weight of the block). This principle is crucial for understanding why each spring balance shows a reading that relates to the weight the spring is supporting.

Tension in Connected Systems

Tension refers to the force transmitted through a rope, string, or in this case, a spring, when it is pulled tight by forces acting from opposite ends. In a system where multiple spring balances are connected in series, the tension is transmitted throughout the system. Understanding how tension is distributed helps explain why each spring balance reads the same tension value, as the force from the hanging block is conveyed through each balance in the chain.

Operation of Spring Balances

Spring balances operate based on Hooke's Law, where the extension of the spring is proportional to the load applied, within the elastic limit. The reading on a spring balance represents the tension in the spring. This concept is important because it explains how the device measures force, and why, in a vertically hanging system under static conditions, each spring balance reflects the force (or equivalent mass) being applied to it.

Free-Body Diagrams and Force Analysis

This concept involves breaking down a complex system into simpler parts to analyze the forces acting on each component. By drawing free-body diagrams, one can isolate the forces acting on the block and on each spring balance, simplifying the analysis of tension forces and leading to the correct understanding that the upper spring balance supports the same force as the lower one when the masses of the spring balances are negligible.

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