Question

n 4. It's a "Seconds Pendulum!" A seconds pendulum is a simple pendulum that crosses its equilibrium position once every (a) Find the length of this pendulum. b) Our definition for the length of a meter is the distance light travels in 1/299,792, 458 s. Given your answer to part a), why do you think we don't just use the length of a seconds pendulum as our standard for the definition of a meter instead? (c) Given that the length of a seconds pendulum is 0.9927 m in Tokyo, Japan, and 0.9942 m in Cambridge, England, how much longer would it take for a penny to fall from a 100m building in Tokyo than in Cambridge? Solutioin

Answer 1

(a) T = 2*pi * sqrt (L/g)

taking g as 9.8 m/s2 and T as 2 seconds

L = 0.9929 m

(b) The idea of defining the meter as the length of a seconds pendulum was not a good idea, because gravity is different by a small but significant amount (about 0.3%) between equator and poles, so the length of the meter would also have varied..

(c) In Tokyo,

2 = 2*pi sqrt ( 0.9927 / g)

g = 9.7975 m/s2

In cambridge,

2 = 2*pi sqrt ( 0.9942 / g)

g = 9.812 m/s2

so,

we can see that g value is more in cambridge,

time taken by penny

In tokyo = sqrt (2h / g) = 4.518 sec

In cambridge, 4.514 sec

so, it will take 4e-3 seconds more (or 4 ms)