**Introduction:**
In this problem, we are given the specific gravity of a wooden cylinder and the specific gravity of oil. We need to find the L/D ratio (length-to-diameter ratio) for the cylinder to float with its longitudinal axis vertical in oil.

**Understanding the Problem:**
To solve this problem, we need to consider the buoyancy force acting on the wooden cylinder and the weight of the cylinder. If the buoyancy force is greater than or equal to the weight of the cylinder, it will float in oil.

**Calculating the Volume:**
The first step is to calculate the volume of the wooden cylinder. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. Since the cylinder is circular in cross-section, the radius is equal to half the diameter. Let's assume the diameter of the cylinder is D.

**Calculating the Weight:**
The weight of the wooden cylinder can be calculated using the formula W = mg, where m is the mass of the cylinder and g is the acceleration due to gravity. The mass of the cylinder can be calculated using the formula m = ρV, where ρ is the density of wood and V is the volume of the cylinder.

**Calculating the Buoyancy Force:**
The buoyancy force can be calculated using the formula F_buoyancy = ρ_fluid * V * g, where ρ_fluid is the density of the fluid (in this case, oil) and V is the volume of the fluid displaced by the cylinder.

**Setting up the Equation:**
To determine the L/D ratio for the cylinder to float, we need to equate the weight of the cylinder to the buoyancy force. This can be written as W = F_buoyancy. Rearranging the equation, we get ρ_wood * V * g = ρ_fluid * V * g.

**Simplifying the Equation:**
Since the density of wood and the density of oil are given, we can substitute these values into the equation. The density of wood can be calculated using the specific gravity, which is the ratio of the density of the material to the density of water. The density of oil is given. After substituting the values, the equation simplifies to specific gravity of wood * V = specific gravity of oil * V.

**Calculating the L/D Ratio:**
To find the L/D ratio, we can cancel out the volume V from both sides of the equation. This gives us specific gravity of wood = specific gravity of oil. Since we know the specific gravity of wood and oil, we can substitute these values into the equation and solve for the L/D ratio.

**Conclusion:**
In conclusion, the L/D ratio for the wooden cylinder to float with its longitudinal axis vertical in oil can be calculated by equating the weight of the cylinder to the buoyancy force. By substituting the specific gravities of wood and oil into the equation, we can solve for the L/D ratio.