Final answer:
The force exerted by a bicycle chain on gears of different sizes depends on several factors, including the radius of the gear and the tension in the chain. However, without additional context or formulas, a specific force cannot be determined, and none of the provided options (1/2 T, 2/3 T, 3/4 T, 4/5 T) can be confidently selected.
Step-by-step explanation:
When comparing the force exerted by a bicycle chain on gears of different sizes, it is assumed that the tension in the chain remains constant. However, the actual force exerted by the chain will vary depending on the radius of the gear it is attached to. The question mentions specific radii for the smallest and the largest gears, but does not provide enough information to directly calculate the forces involved. This may be a concept question, exploring the relationship between gear size and force exerted, rather than a calculation problem. Typically, the tension in the chain distributed over the gear's circumference provides the force that turns the gear. If the tension is the same, the force exerted by a smaller gear would be greater than that by a larger gear because the smaller radius results in a higher pressure (force per unit area).
However, the options provided (1/2 T, 2/3 T, 3/4 T, 4/5 T) suggest a proportionality that cannot be determined with the given information. Without additional context or a formula linking gear size to chain force, this question cannot be accurately answered. Assuming constant chain tension and ignoring other factors like friction and the mechanical advantage provided by different gear sizes, the force exerted by the chain on each gear cannot be assumed to be a simple fraction of T.