By using simple harmonic motion concept, The length of a simple pendulum on earth will be 63.6 cm.
Simple pendulum exhibits simple harmonic motion. According to the simple harmonic motion we have,
Length of pendulum (L) = [tex]\frac{T^{2}g }{4\pi ^{2} }[/tex]
where, T is time period of the pendulum and g is the gravity.
at earth we have g value 9.8 m/s^2 . g is also considered as a acceleration due to gravitational force.
Keeping the appropriate values, we get
Length of pendulum (L) = [tex]\frac{1.6^{2} * 9.8 }{4 * 3.14^{2} }[/tex]
L = 0.636 meter = 0.636x100 cm (1 meter = 100 centimeter)
Hence the length of the pendulum will be 63.6 cm.
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