3: Three identical springs are shown in figure. When a 4 kg mass is suspended from spring A, it

step 1 Hello and welcome to this video solution of numerate. Here we are given that we have got three i

3: Three identical springs are shown in figure. When a 4 kg...

3: Three identical springs are shown in figure. When a $4 \mathrm{~kg}$ mass is suspended from spring $\mathrm{A}$, its length increases by $1 \mathrm{~cm}$. Now if a $6 \mathrm{~kg}$ mass is suspended from the free end of spring $\mathrm{C}$, then increase in its length is $\ldots \ldots \mathrm{cm}$. (A) $1.5$ (B) $3.0$ (C) $4.5$ (D) $6.0$

Key Concepts

Hooke's Law

Hooke's law states that the extension or compression (?x) of an elastic spring is directly proportional to the force (F) applied to it, provided the elastic limit is not exceeded. This relationship is commonly written as F = k?x, where k is the spring constant. This principle is central to understanding the behavior of springs under applied loads.

Spring Constant

The spring constant (k) is a measure of a spring's stiffness and defines the relationship between the force applied to the spring and its resulting displacement. It is determined experimentally by measuring how much the spring stretches under a known load. Once k is known for a single spring, it can be used to predict the behavior of systems where such springs are combined in various configurations.

Series Combination of Springs

When springs are connected in series, they effectively share the same load and the overall displacement is the sum of the individual displacements. Mathematically, the effective spring constant of springs in series is given by the reciprocal of the sum of the reciprocals of their individual spring constants. For two identical springs, this simplifies to an effective spring constant of k/2, meaning that the system is less stiff and will stretch twice as much as a single spring under the same load.

Gravitational Force

Gravitational force is the force exerted on a mass by the Earth, calculated as mg (mass times the acceleration due to gravity). In problems involving suspended masses and springs, gravitational force is the load that causes the spring to stretch. Understanding this force is essential to applying Hooke’s law to real-world situations involving weights.

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