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 the spring of length $l_{2}$ is (a) $k(1+n)$ (b) $\frac{(n+1) k}{n}$ (c) $k$ (d) $k /(n+1)$

Name: Problem 47, Chapter 15: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-14T21:02:05-08:00
Duration: 45 s
Channel: Hunza Gilgit
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 the spring of length l2 is (a) k(1+n) (b) ((n+1) k)/(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 the spring of length $l_{2}$ is
(a) $k(1+n)$
(b) $\frac{(n+1) k}{n}$
(c) $k$
(d) $k /(n+1)$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 15, Problem 47

Instant Answer

Solved by Expert Hunza Gilgit

01/14/2022

Step 1

This means that if we cut a spring into two parts, the force constant of each part will be greater than the original spring. Show more…

Show all steps

Thanks for your feedback!

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 the spring of length $l_{2}$ is (a) $k(1+n)$ (b) $\frac{(n+1) k}{n}$ (c) $k$ (d) $k /(n+1)$

Play audio

Feedback

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Uniformity of Material Properties in Springs

The analysis of a cut spring assumes that the material and cross-sectional area are uniform throughout the spring. This uniformity means that when the spring is divided, the intrinsic properties affecting stiffness remain the same, and only the length factor influences the new spring constant for each segment.

Spring Constant and Length Relationship

A spring's force constant (k) is determined by its material properties and dimensions, specifically being inversely proportional to its length. When a uniform spring is divided into smaller segments, each segment's force constant adjusts according to its new length, with shorter segments exhibiting a higher force constant because the same material is now concentrated over a smaller length.

Please give Ace some feedback