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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 unscratched. 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 can have maximum extension x. Now, accroding to law of energy conservation we can write,
Decrease in gravitational potential energy of mass=increase in potential energy of spring.
mgx=12kx2
x=2mgk
Here gravitational potential energy of mass decreases as the mass moves down.

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