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Question

An ideal spring with spring constant k is hung from the ceiling and a block of mass m is attached to its lower end. The mass is released with the spring initially unstretched. The maximum extension in the spring is

A
4mgk
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B
2mgk
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C
mgk
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D
mg2k
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Solution

The correct option is B 2mgk
Let the spring extend in length y when mass m is hung freely at its lower end.
The elastic potential energy stored in the spring =12ky2
when the mass is released, the gravitational potential energy lost is =mgy
From energy conservation principle,
Increase in elastic
PE = Decrease in Gravitational PE
=12ky2=mgyy=2mgk
Hence, the correct answer is option (b).

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