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## Homework Statement

Which is a more accurate way of measuring g, the acceleration due to gravity? Using a bar pendulum or a simple pendulum?

## Homework Equations

Bar Pendulum = metal rod with slotted holes at fixed distances, which serve as pivots.

## The Attempt at a Solution

For small oscillations, the time periods of both the bar pendulum and the simple pendulum have identical mathematical forms. But, I am not able to decide which one would be a better device for measuring g (by measuring the time period for a fixed number of oscillations, say 20, by varying the effective lengths).

Advantages of bar pendulum over simple pendulum: is rigid, so motion is confined (mostly) to 2D; the string of the simple pendulum may not remain straight at maximum angular displacements, but there is no such problem with the bar pendulum (again assuming that it remains fairly rigid over the small angular displacements).

Advantages of simple pendulum over a bar pendulum: Most of the mass is concentrated in the bob and so the nonuniform mass distribution can be neglected. The point of support (pivot) is well defined and there is negligible friction due to the pivot (and the string wrapped around it). However, for a rod pivoted on a knife edge arrangement, the point of support is not well defined. Further, there may be friction which leads to lateral displacement of the point of support and so the mean position may not be laterally fixed.

Thanks for your help.

Cheers

Vivek