A solid cylinder of height `h` and mass `m` is floating in a liquid of density `rho` as shown in the figure. Find the acceleration of the vessel (in `m//s^(2)`) containing liquid for which the relative downward acceleration of the completely immersed cylinder w.r.t. vessel becomes equal to one-third of that of the vessel. (Take `g = 10 m//s^(2))

Explanation

To solve the problem, we need to analyze the forces acting on the solid cylinder that is floating in the liquid, and how the acceleration of the vessel affects the cylinder's motion.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a solid cylinder of height `h` and mass `m` floating in a liquid of density `ρ`.
- The cylinder is partially submerged in the liquid. The problem states that the relative downward acceleration of the completely immersed cylinder with respect to the vessel is one-third of the vessel's acceleration.

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