A cylindrical wooden cork of mass 250 g and cross sectional area 10 `cm^(2)` is floating into a beaker filled with water, with an extra weight of 30 g attached to its bottom, as shown in the adjoining figure. If the cork Performs, S.H.M., determine its frequency. take,
Specific gravity of wood = 0.30
`g = 9.8 m//s^(2)`

Explanation

To solve the problem, we need to determine the frequency of the simple harmonic motion (SHM) of the floating cork with an attached weight. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the System
- The cork has a mass \( M = 250 \, \text{g} = 0.25 \, \text{kg} \).
- An additional weight \( m = 30 \, \text{g} = 0.03 \, \text{kg} \) is attached to the cork.
- The total mass \( M + m = 0.25 \, \text{kg} + 0.03 \, \text{kg} = 0.28 \, \text{kg} \).
- The cross-sectional area of the cork is \( A = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 = 10^{-3} \, \text{m}^2 \).

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