The most common limit gage used for inspecting the hole diameter is

The correct option is Plug gage.

Here is a step-by-step educational explanation of why this option is correct:

1. What is a Limit Gage?
Limit gages are inspection tools used in manufacturing to quickly verify whether a part's dimension falls within its specified limits (the minimum and maximum allowable sizes). They typically operate on a "Go / No-Go" principle, meaning one end of the gage must fit into or over the part (the "Go" side), while the other end must not (the "No-Go" side).

2. Understanding the Options:
• Plug Gage: A plug gage is a cylindrical tool designed specifically to check the internal dimensions of a workpiece, such as a hole diameter. The "Go" plug checks the lower limit of the hole diameter (and must enter the hole), while the "No-Go" plug checks the upper limit (and must not enter the hole). Because it is inserted directly into the hole, it is the most common limit gage used for inspecting hole diameters.
• Ring Gage: A ring gage has a precise circular opening and is used to inspect the external diameter of cylindrical parts like shafts. It cannot be used to measure internal holes.
• Snap Gage: A snap gage is a C-shaped frame with measuring jaws. It is used to check external dimensions (such as the outer diameter of a shaft or the thickness of a plate) by trying to "snap" it over the workpiece.
• Master Gage: A master gage is an extremely precise reference standard. It is used to calibrate, check, or set other working gages (like plug gages or micrometers) rather than being used for routine inspection of workpieces on the production line.

Conclusion:
Since the task is to inspect the internal diameter of a hole, a plug gage is the standard and most commonly used limit gage for this purpose.