Oscillations - Result Question 37
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
(a) $1: 9$
(b) $1: 11$
(c) $1: 14$
(d) $1: 6$
[2017]
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Answer:
Correct Answer: 41. (b)
Solution:
- (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 $k_3=2 k$
