First slide

Simple hormonic motion

Question

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

Moderate

A

$(2 / 3) k$
B

$(3/2) k$
C

3K
D

6K

Solution

$Length of first piece = l / 3 Length of second piece = 2 I I 3 By definition, a force of maguitude t is required to elonSate or compress the spring of length / by unity . So theelongationinthepieceoflength 2 llSwou \ dbe 2 / 3 units . Now, for (2 / 3) unit elongatiotr, the force needed is k . So, for unit elongation . the force needed wold be \frac{k}{(2 / 3)} = \frac{3 k}{2} . This is force constant, by definition.$

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