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Two masses are connected by a spring as shown in the figure. One of the masses is given a velocity $v = 2k$, where $k$ is the spring constant. Then the maximum extension in the spring will be: A. 2 m B. m C. 2mk D. 3mk

1. 2 m
2. m
3. 2mk
4. 3mk

Correct answer: 2mk

Solution

The system is isolated on a smooth surface, so mechanical energy is conserved. The initial kinetic energy of the moving mass is converted into spring potential energy at maximum extension. Using the given relation in the question, the maximum extension comes out to be $2mk$.

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