Published by:
CGP EDU Academic Team
Published on: September 12, 2026
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 
where, 
and n is an integer. The ratio 
of the corresponding force constants, 
and 
will be:
Text Solution
Verified by ExpertsThe correct answer is:
A
To find the ratio of the force constants of the two spring segments, we can apply the relation of spring constants to their lengths.
Now substituting l1 = nl2 into the expression for k1:
We now take the ratio of the two force constants:
\frac{k1}{k2} = \frac{\frac{k}{nl2}}{\frac{k}{l2}} = \frac{1}{n}
Hence, the ratio of the force constants is \frac{k1}{k2} = \frac{1}{n}. Therefore, option A is correct.
- The force constant of a spring is inversely proportional to its length. Therefore, if the initial spring length is l and is split into l1 and l2, where l1 = nl2, we have:
- k1 = \frac{k}{l1}
- k2 = \frac{k}{l2}
Now substituting l1 = nl2 into the expression for k1:
- k1 = \frac{k}{nl2}
- k2 = \frac{k}{l2}
We now take the ratio of the two force constants:
\frac{k1}{k2} = \frac{\frac{k}{nl2}}{\frac{k}{l2}} = \frac{1}{n}
Hence, the ratio of the force constants is \frac{k1}{k2} = \frac{1}{n}. Therefore, option A is correct.
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