what is the vibration period of the sample pendulum at the top of mountain, at sea level, and in a deep mine.

Answer 1

practically it is almost the same (you are not going to notice milisecond differences)... but gravitational force will be lesser the further you are from the center of the earth.

T= 2 pi sqrt (l/g)
g=G*m1/r^2
since G decreases the further you are from the center of the earth. (the actual center of gravity is slightly off center though)
T will be longer on a mountain, vs at sea level and if the deep mine is underground below sea level, it should be the shortest of the 3...

(you really need to be able to detect milisecond differences though)

Answer 2

you're able to evaluate that the mountains might take in quantity interior the sea, so the water might upward thrust some. via undeniable fact that i can basically make an assumption that the oceans could be approximately 9000 feet deep. for sure, there is not any thank you to tell for advantageous with out calculating the quantity of the mountains, quantity of the trenches and quantity of the undersea mountains.

Answer 3

value of g decreases in deep mines and going to higher altitudes hence time period is minimum at sea level and increases as you go up or down.

Answer 4

The period of a pendulum is inversely proportional to the square root of g:
http://en.wikipedia.org/wiki/Pendulum

So, you just need to figure out g at different altitudes.