The length of the second pendulum on earth is 1m and on the moon 1/6m.
Given:
The time period of a second pendulum T = 2s
By using the formula T = 2π √l/g we can calculate the length of the pendulum on earth and the moon.
Here g = acceleration due to gravity and
l = the length of the pendulum.
Now
l = g(T/ 2π)^2
l = 9.8 m/s^2(2s / 2 x 3.14)^2
le = 1 m
Now calculate the length of the pendulum on the moon
T = 2π √lm/gm ∴ gm = ge/6
Now putting the value of g we get.
or 2 = 2 π √lm / ge/6
2 = 2 π √6lm / π ^2le
lm = le/6
now given le = 1m
lm = 1/6 m
Thus the length of the second pendulum on earth is 1m and on the moon 1/6m.
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