Pendulum A located on the earth and pendulum B located on another planet have the same period for small angle oscillations. What is the ratio of the length of pendulum A to the length of pendulum B? The acceleration due to the gravity on the surface of the planet is 1.6m/s2.
Time period of a pendulum is given by:
T = 2*pi*sqrt (L/g)
Given that Both pendulum A and B have same period, So that means:
Time period on planet A = Time period on planet B
Ta = Tb
2*pi*sqrt (La/ga) = 2*pi*sqrt (Lb/gb)
La/Lb = ga/gb
Now we know that ga = acceleration due to gravity on earth = 9.8 m/s^2
gb = acceleration due to gravity on another planet = 1.6 m/s^2
L = length of pendulum
So,
La/Lb = ga/gb
La/Lb = 9.8/1.6
La/Lb = 6.125 = 6.1 = ration of length of pendulum
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