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Spring Block's Time Period

A spring of s...

Question

A spring of spring constant 2k and length L is split in to two equal parts. What is the effective spring constant, if both are connected in parallel

A

2k

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B

4k

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C

k

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D

k/2

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Solution

The correct option is B 4k
The restoring force is constant and is independent of the length of the spring.
Using this concept, we have, if $k_{2}$ is the spring constant of the cut spring of length (L/2), then $F = k L = k_{2} (L / 2) ⟹ k_{2} = 2 k$
If these two springs are joined together in parallel, their spring constants gets added up. Thus effective spring constant is $k_{e f f} = 4 k$
The correct option is (b)

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