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Compare the time of a simple pendulum at a place where g is 9.8 ms-2 and 4.36m s-2 respectively

July 28, 2018 2
A simple pendulum is made of a long string and a tiny metal sphere, steel or preferably lead (higher density).  The period of oscillation of a simple pendulum may be found by the formula
T equals 2 straight pi square root of straight l over straight g end root where space straight l space is space lenght space of space pendulam and space straight g space is space accelation space toward space gravity
in this question in first case take g=9.8 ms to the power of negative 2 end exponent
and in second case take g=4.36 ms to the power of negative 2 end exponent
here length of string l will same in both case
w h e n space g equals space 9.8 T subscript 1 equals 2 straight pi square root of fraction numerator straight l over denominator 9.8 end fraction end root space space space space space space space space space space........ left parenthesis 1 right parenthesis when space straight g equals 4.36 straight T subscript 2 equals 2 straight pi square root of fraction numerator straight l over denominator 4.36 end fraction end root space space space space space space space space space......... left parenthesis 2 right parenthesis straight T subscript 1 over straight T subscript 2 equals fraction numerator 2 straight pi square root of fraction numerator straight l over denominator 9.8 end fraction end root space space space space over denominator 2 straight pi square root of fraction numerator straight l over denominator 4.36 end fraction end root space end fraction equals square root of fraction numerator 4.36 over denominator 9.8 end fraction end root equals square root of fraction numerator 1 over denominator 2.24 end fraction end root equals fraction numerator 1 over denominator 1.499 end fraction straight T subscript 2 equals 1.499 space straight T subscript 1
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