Question: Under certain conditions, the period \(T\) of a clock pendulum (i.e., the time required for one back-and-forth movement) is given in terms of its length \(L\) by \(T=2 \pi \sqrt{L / g}\), where \(g\) is the constant acceleration due to gravity.

1. Assuming that the length of a clock pendulum can vary (say, due to temperature changes), find the rate of change of the period \(T\) with respect to the length \(L\).
2. If \(L\) is in meters \((\mathrm{m})\) and \(T\) is in seconds (s), what are the units for the rate of change in part (a)?
3. If a pendulum clock is running slow, should the length of the pendulum be increased or decreased to correct the problem?
4. The constant \(g\) generally decreases with altitude. If you move a pendulum clock from sea level to a higher elevation, will it run faster or slower?
5. Assuming the length of the pendulum to be constant, find the rate of change of the period \(T\) with respect to \(g\).
6. Assuming that \(T\) is in seconds (s) and \(g\) is in meters per second squared \(\left(\mathrm{m} / \mathrm{s}^{2}\right)\), find the units for the rate of change in part (e).

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document