A uniform spring has an unstretched length L and a force constant k . The spring is cut into two parts of unstretched lengths l 1 and l 2 such that l 2 = η l 2 , where η is an integer. The corresponding force constants are k 1 and k 2 , then

Question

A uniform spring has an unstretched length L and a force constant k . The spring is cut into two parts of unstretched lengths l 1 and l 2 such that l 2 = η l 2 , where η is an integer. The corresponding force constants are k 1 and k 2 , then, force has to be kept same to find k 1 and k 2, k 1 = k η + 1 η and k 2 = k η - 1, k 1 = k η - 1 η and k 2 = k η + 1, k 1 = k η + 1 η and k 2 = k η + 1

MARKS App · Accepted Answer

In case of cutting of a spring, l × k = c o n s t a n t k 1 l 1 = k 2 l 2 k 1 η l 2 = k 2 l 2 ⇒ η k 1 = k 2 ...............(1) Now both the springs when connected in series should give the same effect as that of the original spring. Hence, by applying the concept of springs connected in series, we obtain, 1 k = 1 k 1 + 1 k 2 ...............(2) 1 k = 1 k 1 + 1 η k 1 ⇒ k 1 k = η + 1 η (using (1)) k 1 = η + 1 η k ............(3) Using (3) again in (2), we obtain, k 2 = η + 1 k

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