if a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when?

Question

moved to the top of the moutain? explain

Answer 1

The period of a pendulum is T = 2π √(L/g) where L is its length and g is the local gravitational field strength.

At the top of the mountain, g will be slightly less than at the base (g = GM/r^2 where r is the distance from the centre of the earth to the surface). Therefore the period of the pendulum will be slightly more, and it will not keep perfect time.

Answer 2

Probably not.
The period of a pendulum depends on gravity, approximately according to the inverse square of the gravitational acceleration.
The gravity at the top of the mountain is less than that at the base. Therefore the period will be slightly longer. Ordinarily, this will be the major effect.

However, you could argue that since the air density is lower, you might be able to construct the pendulum bob in such a way that the reduced air friction would exactly compensate for the reduced gravity and the period would remain the same.

Also, since typically the air temperature falls as you gain altitude, you might be able to construct the pendulum arm so that the length changed by just enough to compensate for the reduced gravity.

There might be other compensation schemes too. But put it this way: if the environment around the clock is identical at the base and the top of the mountain, excepting only the change in gravity, then the clock will run a little bit slower.

Answer 3

Yes it will, If it is set for Mountain Time it will stay perfect until the Lunar Equinox. Now in the middle of the mountain is where you will need to lengthen the pendulum in direct proportion to the barometric pressure on the fulcrum.

Answer 4

No. Gravitation force (g) is one component to the time it takes for one motion of the pendulum, and g is slightly less at the top of the mountain.

Answer 5

who cares