Oscillations - Result Question 37

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41. A spring of force constant $k$ is cut into lengths of ratio $1: 2: 3$. They are connected in series and the new force constant is $k^{\prime}$. Then they are connected in parallel and force constant is $k^{\prime \prime}$. Then $k^{\prime}: k^{\prime \prime}$ is

======= ####41. A spring of force constant $k$ is cut into lengths of ratio $1: 2: 3$. They are connected in series and the new force constant is $k^{\prime}$. Then they are connected in parallel and force constant is $k^{\prime \prime}$. Then $k^{\prime}: k^{\prime \prime}$ is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/oscillations/oscillations—result-question-37.md (a) $1: 9$

(b) $1: 11$

(c) $1: 14$

(d) $1: 6$

[2017]

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Answer:

Correct Answer: 41. (b)

Solution:

  1. (b) Let $\ell$ be the complete length of the spring. Length when cut in ratio, $1: 2: 3$ are

$\frac{\ell}{6}, \frac{\ell}{3}$ and $\frac{\ell}{2}$

Spring constant $(k) \propto \frac{1}{\text{ length }(\ell)}$

Spring constant for given segments

$k_1=6 k, k_2=3 k$ and $k_3=2 k$