Question

A pendulum is taken 1km inside the earth from sea level. Then the approximate gain or loss of time of pendulum.
Is the time period of a seconds pendulum always the same i.e; 2 seconds or is it dependent on the surrounding of the system?

Answer 1

At sea level, gravitational constant that is g = GM/R and Time period, T = 2pi*root(l/g) at below 1 km, g’ = GM/(R-1000) T’ = 2pi*root(l/g’) T/T’ = root(g’/g) = > root(R/(R-1000)) T’ = T/root(R/(R-1)) => T/root(6400/6399) = > T/root(1.000156274) => T/1.000078134 or T’ = 0.999921872*T putting value of T for appropriaate T we get T’ approx 13.6 seconds. The time for one complete cycle, a left swing and a right swing, is called the time period. The time period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. since, the amplitude changes in sea(due to viscosity of water) hence time period will change.