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A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

1. 2 Mg/k
2. 4 Mg/k
3. Mg/2k
4. Mg/k

Correct answer: 2 Mg/k

Solution

The maximum extension occurs when the potential energy of the spring equals the gravitational potential energy lost by the block. Using energy conservation, we get Mgx = (1/2)kx^2, solving for x gives x = 2Mg/k.

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