SATHEE: Simple Harmonic Motion 4 Question 1

Simple Harmonic Motion 4 Question 1

1. A spring whose unstretched length is $l$ has a force constant $k$ . The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1} = n l_{2}$ and $n$ is an integer. The ratio $k_{1} / k_{2}$ of the corresponding force constants $k_{1}$ and $k_{2}$ will be

(a) $n$

(b) $\frac{1}{n^{2}}$

(d) $n^{2}$

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Answer:

Correct Answer: 1. (c)

Solution:

If parameters like material, number of loops per unit length, area of cross-section, etc., are kept same, then force constant of spring is inversely proportional to its length.

In given case, all other parameters are same for both parts of spring.

$\begin{aligned} So, & k_{1} & \propto \frac{1}{l_{1}} and k_{2} \propto \frac{1}{l_{2}} \\ ∴ & \frac{k_{1}}{k_{2}} & = \frac{l_{2}}{l_{1}} \\ = \frac{l_{2}}{n l_{2}} = \frac{1}{n} [∵ l_{1} = n l_{2}] \end{aligned}$

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Simple Harmonic Motion 4 Question 1

1. A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l1 and l2 where, l1=nl2 and n is an integer. The ratio k1/k2 of the corresponding force constants k1 and k2 will be

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1. A spring whose unstretched length is $l$ has a force constant $k$ . The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1} = n l_{2}$ and $n$ is an integer. The ratio $k_{1} / k_{2}$ of the corresponding force constants $k_{1}$ and $k_{2}$ will be