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The length of a seconds pendulum is increased by 2%. What is the loss or gain of seconds in a day?

Asked by eshwarnevedh 10th January 2018, 6:51 AM
Answered by Expert
Time period T of simple pendulam is given by begin mathsize 12px style T space equals space 2 pi square root of l over g end root end style , l is length and g is acceleration due to gravity. 
begin mathsize 12px style T space proportional to space square root of l
b y space t a k i n g space log space o n space b o t h space s i d e s comma space ln left parenthesis T right parenthesis space equals space 1 half ln left parenthesis l right parenthesis
i f space w e space d i f f e r n t i a t e space a b o v e comma space fraction numerator d T over denominator T end fraction space equals space 1 half fraction numerator d l over denominator l end fraction
h e n c e space 2 percent sign space i n c l e a s e space i n space l e n g t h space w i l l space m a k e space a n space i n c r e a s e space o f space 1 percent sign space i n space p e r i o d.

t i m e space l o s t space i n space a space d a y space equals space 24 space cross times 60 space cross times 60 space cross times.01 space s e c o n d s space equals space 864 space s e c o n d s end style
Answered by Expert 10th January 2018, 11:20 AM
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