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Does a bigger wheel increases the efficiency of machine in and axle?

A bigger wheel in a wheel and axle system *can* increase efficiency, but it depends on what you mean by "efficiency" and how the system is used.

* Mechanical Advantage: A larger wheel provides a greater mechanical advantage. This means you can lift a heavier load or move a greater resistance with the same amount of effort. In this sense, it's *more efficient* because you get more output for the same input.

* Efficiency (as in %): However, a larger wheel doesn't necessarily increase *efficiency* in the sense of reducing energy loss due to friction. The efficiency (as a percentage) is the ratio of useful work output to total work input. A larger wheel might increase friction in the axle bearings, especially if the system isn't well-lubricated. Therefore, a slightly smaller wheel might, in some specific situations, be *more efficient* due to less friction losses.

In short: a bigger wheel gives you *more leverage* (mechanical advantage), allowing you to do more work with less input force. But, whether that translates into *higher overall efficiency* (reducing energy losses) depends on the specific design and frictional forces involved.