Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

Options

A. `1:2`
B. `3:2`
C. `3:1`
D. `2:3`

Explanation

To solve the problem, we need to find the ratio of the amplitudes of two oscillating masses attached to springs with different spring constants, given that their maximum velocities are equal.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Spring constants: \( k_1 = 2k \) and \( k_2 = 9k \)
- Masses: \( m_1 = 50 \, \text{g} = 0.05 \, \text{kg} \) and \( m_2 = 100 \, \text{g} = 0.1 \, \text{kg} \)

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