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A massless spring of spring constant k and natural length L0 has one end fixed and the other end attached to a small mass m resting on a frictionless table, with the spring horizontal. The mass is made to revolve at angular velocity omega about the fixed end. Find the elongation of the spring.

1. (k - m*omega²*L0) / (m*omega²)
2. (m*omega²*L0) / (k + m*omega²)
3. (m*omega²*L0) / (k - m*omega²)
4. (k + m*omega²*L0) / (m*omega²)

Correct answer: (m*omega²*L0) / (k - m*omega²)

Solution

The stretched length is L0 + x, and the spring force k*x provides the centripetal force m*omega²*(L0 + x). Solving k*x = m*omega²*(L0 + x) gives x = m*omega²*L0 / (k - m*omega²).

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