A wooden stick of length `L`, radius `R` and density `rho` has a small metal piece of mass `m` ( of negligible volume) atached to its one end. Find the minimum value for the mass `m` (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density `sigma(gtrho)`.

Explanation

To solve the problem of finding the minimum mass \( m \) that would make the wooden stick float vertically in equilibrium in a liquid of density \( \sigma \) (where \( \sigma > \rho \)), we can follow these steps:

### Step 1: Understand the forces acting on the system
When the stick is floating, the total weight of the stick and the attached mass must equal the buoyant force exerted by the liquid. The forces acting on the system are:
- Weight of the stick
- Weight of the mass \( m \)
- Buoyant force from the liquid

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