Spring Systems question from MHT CET 2026 (14 May, Shift 1)

Answer: (c)

1. Spring unstretched at the top, so amplitude = static extension: $A = \frac{mg}{k} = \frac{g}{\omega^2}$.
2. $v_{max} = A\omega = \frac{g}{\omega}$, with $\omega = 2\pi f = 20\pi$ rad/s.
3. $v_{max} = \frac{10}{20\pi} = \frac{1}{2\pi}$ m/s
4. So the answer is (c) $\frac{1}{2\pi}$ m/s.