Question

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) \( \frac{2 m g}{k} \)

(2) \( \frac{m g}{k} \)

(3) \( \frac{3 m g}{2 k} \)

(4) \( \frac{m g}{2 k} \)

Answer 1

The correct option is (1) \(\frac{2mg}{k}\)

For the maximum extension:

\(mgx_{max} = \frac{1}{2} mx^2_{max}\)

\(x_{max} = \frac{2mg}{k}\)

Hence, for the maximum extension of spring will be \(\frac{2mg}{k}\)