A grandfather clock measures time by counting the number of oscillations of a small-angle pendulum. You take a grandfather clock that gives the correct time at sea level (where g = 9.81 m/s 2 ) up a mountain and notice that after two days it is running five minutes behind. What is the value of the gravitational acceleration up that mountain?
I tried solving this by using $T = \sqrt{l/g}$ and setting up the difference of the reciprocals times the time (2 days) but I got an answer depended on the length of the pendulum. How do I solve this?
Hint: assuming that the length are the same at each elevation you can set up a relationship between the tworld periods like this: $$\frac{T_2}{T_1}=\frac{\sqrt{g_1}}{\sqrt{g_2}}$$