Question

Will a pendulum clock gain or lose time when taken to the top of a mountain?

Answer 1

we know, time period is given by , T = 2π√{l/g}
where l is length of bob of simple pendulum and g is acceleration due to gravity.

at the top of mountain,
acceleration due to gravity , decreases. so, time period increases.

[ As you know, from gravitational law, g' = g/(1 + h/r)² , where h is height of top of mountain from the ground and r is the radius of the earth., here it is clear that at the top of mountain, acceleration due to gravity decreases. ]

time period increases means to say tim taken to complete one oscillation increases . And hence, clock lose time.

Answer 2

Explanation:

Derive the equation for the kinetic energy and potential energy of a simple harmonic oscillator and show that the total energy of a particle in simple harmonic motion is constant at any point on its path