Simple Harmonic Motion 4 Question 10

10. A spring of force constant $k$ is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(1999, 2M)

(a) $\frac{2}{3} k$

(b) $\frac{3}{2} k$

(c) $3 k$

(d) $6 k$

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Answer:

Correct Answer: 10. (b)

Solution:

  1. $l _1=2 l _2 \quad \therefore \quad l _1=\frac{2}{3} l$

$$ \therefore \quad k _1=\frac{3}{2} k $$

Force constant $k \propto \frac{1}{\text { length of spring }}$



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