Introduction:
When a block of iron floats in mercury, the fraction of its volume submerged depends on the temperature of the system. In this case, we are given that the block of iron floats in mercury at two different temperatures, 0 degrees Celsius and 60 degrees Celsius. We are also given the coefficient of volume expansion of iron, denoted as YFe.

Understanding the problem:
To find the ratio of K1/K2, we need to understand what K1 and K2 represent. K1 represents the fraction of the iron block's volume submerged at 0 degrees Celsius, while K2 represents the fraction of the iron block's volume submerged at 60 degrees Celsius. We need to find the ratio of these two fractions, i.e., K1/K2.

Relationship between volume expansion and buoyancy:
When an object is submerged in a fluid, it experiences a buoyant force. The magnitude of this buoyant force is equal to the weight of the fluid displaced by the object. For an object to float, the buoyant force acting on it must be equal to or greater than its weight.

The volume of the fluid displaced by the object depends on the volume of the object submerged. If the volume of the object submerged increases, the buoyant force also increases. Therefore, to determine the fraction of an object's volume submerged, we need to consider the relationship between the volume expansion of the object and the buoyant force.

Effect of temperature on the volume of the iron block:
The volume of an object expands with an increase in temperature. This expansion can be quantified using the coefficient of volume expansion, which is a characteristic property of the material.

In this case, the coefficient of volume expansion of iron is given as YFe. This means that for every 1-degree Celsius increase in temperature, the volume of the iron block increases by YFe times its original volume. Similarly, for a decrease in temperature, the volume decreases by YFe times its original volume.

Determining the ratio of K1/K2:
To find the ratio of K1/K2, we need to consider the buoyant force acting on the iron block at the two different temperatures.

At 0 degrees Celsius, the fraction of the iron block's volume submerged is K1. This means that K1 * V, where V is the original volume of the iron block, is equal to the volume of the fluid displaced by the submerged portion of the iron block.

At 60 degrees Celsius, the fraction of the iron block's volume submerged is K2. This means that K2 * V is equal to the volume of the fluid displaced by the submerged portion of the iron block.

Since the buoyant force acting on the iron block is determined by the volume of the fluid displaced, we can equate the buoyant forces at the two temperatures:

K1 * V * ρg = K2 * V * ρg

Here, ρ is the density of mercury and g is the acceleration due to gravity. Since ρ and g are constant, they cancel out from both sides of the equation.

This leaves us with K1 = K2, which implies that the ratio of K1/K2 is 1.

Conclusion:
In conclusion, when a block of iron floats in mercury at zero degrees Celsius and 60 degrees Celsius, the ratio of the fractions of