Question

A simple spring has length $l$ and force constant $k$. It is cut into two springs of length $l_{1}$ and $l_{2}$ such that $l_{1}=n l_{2}(n=$ an integer $)$. The force constant of spring of length $l_{1}$ is: (a) $k(1+n)$ (b) $(k / n)(1+n)$ (c) $k$ (d) $k / n+1$

Name: Problem 58, Chapter 10: Objective Physics : NEET 2020 Examination textbook Gurukul Oswal
Uploaded: 2021-10-04T14:55:41-08:00
Duration: 1 min 31 s
Channel: Ankur S
Description: A simple spring has length l and force constant k. It is cut into two springs of length l1 and l2 such that l1=n l2(n= an integer ). The force constant of spring of length l1 is: (a) k(1+n) (b) (k / n)(1+n) (c) k (d) k / n+1

   A simple spring has length $l$ and force constant $k$. It is cut into two springs of length $l_{1}$ and $l_{2}$ such that $l_{1}=n l_{2}(n=$ an integer $)$. The force constant of spring of length $l_{1}$ is:
(a) $k(1+n)$
(b) $(k / n)(1+n)$
(c) $k$
(d) $k / n+1$

Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

Gurukul Oswal… 2020 Edition

Chapter 10, Problem 58

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Solved by Expert Ankur S

10/04/2021

Step 1

This spring is cut into two springs of lengths $l_{1}$ and $l_{2}$ such that $l_{1}=n l_{2}$ where $n$ is an integer. We are asked to find the force constant of the spring of length $l_{1}$. Show more…

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A simple spring has length $l$ and force constant $k$. It is cut into two springs of length $l_{1}$ and $l_{2}$ such that $l_{1}=n l_{2}(n=$ an integer $)$. The force constant of spring of length $l_{1}$ is: (a) $k(1+n)$ (b) $(k / n)(1+n)$ (c) $k$ (d) $k / n+1$

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Key Concepts

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from equilibrium, with the proportionality constant given by the spring constant. This fundamental relation (F = -kx) underpins the study of elastic systems and describes how springs store mechanical energy and respond to applied forces, making it critical for analyzing and predicting spring behavior in various contexts.

Dependence of the Spring Constant on Length

In a uniform spring, the spring constant is inversely proportional to its length. When a spring is cut into shorter segments, each segment becomes stiffer—that is, it has a higher spring constant—because the force needed to achieve the same displacement is greater. This concept is essential when modifying a spring's dimensions, as it allows one to relate the spring constant of a partial length to that of the original spring.

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