Step 1: Understanding the Concept:
Engine balancing involves neutralizing the forces and moments generated by the reciprocating masses (piston, wrist pin, part of the connecting rod) and rotating masses (crankpin, crank webs, part of the connecting rod).
Imbalances are categorized into primary (acting at engine speed, $\omega$) and secondary (acting at twice engine speed, $2\omega$) forces and couples.
Step 2: Detailed Explanation:
Let us analyze the configuration of different engines.
1.Single-Cylinder Engine: The reciprocating mass creates a primary force along the cylinder axis.
Adding counterweights to the crankshaft can balance the rotating forces and up to $50\%$ of the primary reciprocating force.
However, balancing more than $50\%$ of the primary force creates an equal, unbalanced transverse force perpendicular to the cylinder axis.
Thus, a single-cylinder engine cannot be fully balanced by crankshaft counterweights alone.
2.Multi-Cylinder Engines (Two, Three, and Four Cylinders): In these configurations, various combinations of primary forces, secondary forces, and couples remain unbalanced.
For instance, an inline four-cylinder engine has inherently unbalanced secondary vertical forces, which require dual counter-rotating balance shafts to neutralize, not just crankshaft counterweights.
3.Six-Cylinder Inline Engine (E): An inline six-cylinder four-stroke engine is unique.
The cranks are spaced at $120^{\circ}$ intervals, resulting in perfect primary and secondary balance for both forces and moments.
The symmetrical piston movements naturally cancel out all primary and secondary forces and couples.
Therefore, any remaining internal rotational stresses on the shaft are completely resolved by crankshaft counterweights, making the engine naturally fully balanced.
Step 3: Final Answer:
Among the given configurations, only the inline six-cylinder engine (E) achieves complete balance.