Introduction:
In Civil Engineering, the strength and stability of a column are determined by its slenderness ratio. The slenderness ratio is the ratio of the effective length of a column to its radius of gyration. The l/d ratio of a column is the ratio of its length to its diameter.

Given:
Slenderness ratio = 200

To find:
The l/d ratio of the column

Solution:
We know that the slenderness ratio is given by the formula:

Slenderness ratio = Effective length/radius of gyration

For a circular column, the radius of gyration is given by:

Radius of gyration = Diameter/4√3

Substituting this value in the slenderness ratio formula, we get:

Slenderness ratio = Effective length/(Diameter/4√3)

Rearranging this formula, we get:

Effective length = Slenderness ratio x Diameter/4√3

The l/d ratio of the column is given by the formula:

l/d ratio = Length/Diameter

Substituting the value of Effective length from the first formula, we get:

l/d ratio = (Slenderness ratio x Diameter/4√3)/Diameter

Simplifying this formula, we get:

l/d ratio = Slenderness ratio/4√3

Substituting the given value of slenderness ratio, we get:

l/d ratio = 200/4√3

Simplifying this formula, we get:

l/d ratio = 11.55

Therefore, the l/d ratio of the column is 11.55.

Conclusion:
The l/d ratio of a column is an important factor in determining its strength and stability. In this case, we have calculated the l/d ratio of a circular column with hinged ends, given its slenderness ratio.