Explanation:
The given expression 1 - (1/r)r-1 represents the efficiency of an I.C. engine. Let's understand the meaning of this expression and why it represents mechanical efficiency.

Meaning of the expression:
1. The term (1/r)r-1 can be simplified as (1/r)r.
2. Here, 'r' represents the compression ratio of the engine, which is the ratio of the volume of the combustion chamber at the bottom dead center to the volume at the top dead center.
3. The term (1/r)r represents the ratio of the volume at the top dead center to the volume at the bottom dead center, which is the reciprocal of the compression ratio.
4. Therefore, (1/r)r represents the volumetric efficiency of the engine.

Interpretation of the expression:
1. The expression 1 - (1/r)r-1 can be interpreted as 1 minus the volumetric efficiency of the engine.
2. In other words, it represents the inefficiency or the loss in the engine due to the compression process.

Significance of the expression:
1. In an internal combustion engine, the compression process is not perfectly efficient due to various factors such as heat transfer, friction, and leakage.
2. The expression 1 - (1/r)r-1 quantifies this inefficiency by subtracting the volumetric efficiency from 1.
3. The resulting value represents the proportion of the energy lost during the compression process.

Why it represents mechanical efficiency:
1. Mechanical efficiency is defined as the ratio of the useful work output of an engine to the energy input.
2. In the given expression, 1 - (1/r)r-1 represents the energy lost during the compression process, which is not converted into useful work.
3. Therefore, the expression represents the inefficiency of the engine in converting the input energy into useful work.
4. This inefficiency is a characteristic of the mechanical components of the engine such as the piston, cylinder, and valves, hence it represents mechanical efficiency.

Therefore, the correct answer is option 'A' - mechanical efficiency.