If a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when it is moved to the tip of the mountain? explain.

No

Explanation:

The period of a pendulum is given by

where

L is the length of the pendulum

g is the acceleration due to gravity

We see that the period of the pendulum depends on the value of g. However, the value of the gravitational acceleration is different at different locations on Earth. In particular, at the top of the mountain the value of g is slightly lower than the value of g at the base of the mountain; in fact, g is given by

where

G is the gravitational constant

M is the Earth's mass

r is the distance from the Earth's center

so since r is greater at the top of the mountain, g is lower, and therefore the period of the pendulum will be slightly longer.