A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that lon would execute SHM with a time period. `T=2pisqrt((m)/(Apg))` where, m is mass of the body and p is density of the liquid.

Explanation

To show that a cylindrical log of wood executes simple harmonic motion (SHM) with a time period given by \( T = 2\pi \sqrt{\frac{m}{A \rho g}} \), we can follow these steps:

### Step 1: Understand the System
- We have a cylindrical log of wood with height \( h \) and cross-sectional area \( A \) floating in water.
- The log has a mass \( m \) and is subjected to buoyant force when submerged.

**Hint:** Identify the forces acting on the log when it is floating and when it is displaced.

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