A student measures the distance traversed in free fall of a body , initially at rest in a given time. He uses this data to estimate g, If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is ?
 
a) e1 +2e2 
b) e1-2e1

Asked by Amyra B | 10th Oct, 2014, 09:08: PM

Expert Answer:

W e space k n o w space t h a t comma h space equals space u t space plus space 1 half g t squared rightwards double arrow h space space equals space 1 half g t to the power of 2 space end exponent space space space open square brackets u space equals 0 comma space a s space t h e space b o d y space i s space i n i t i a l l y space a t space r e s t close square brackets rightwards double arrow g space equals space fraction numerator 2 h over denominator t squared end fraction T a k i n g space n a t u r a l space log a r i t h m space o n space b o t h space s i d e s comma space w e space g e t I n space g space equals space ln space h space minus space 2 space ln space t D i f f e r e n t i a t i n g comma fraction numerator increment g over denominator g end fraction equals space fraction numerator increment h over denominator h end fraction minus space 2 fraction numerator increment t over denominator t end fraction F o r space m a x i m u m space p e r m i s s i b l e space e r r o r comma rightwards double arrow open parentheses fraction numerator increment g over denominator g end fraction cross times 100 close parentheses subscript m a x end subscript space equals space open parentheses fraction numerator increment h over denominator h end fraction cross times 100 close parentheses space plus 2 space open parentheses fraction numerator increment t over denominator t end fraction cross times 100 close parentheses A c c o r d i n g space t o space q u e s t i o n comma space open parentheses fraction numerator increment h over denominator h end fraction cross times 100 close parentheses equals space e subscript 1 space a n d space open parentheses fraction numerator increment t over denominator t end fraction cross times 100 close parentheses equals space e o r comma space space open parentheses fraction numerator increment g over denominator g end fraction cross times 100 close parentheses subscript m a x end subscript space equals e subscript 1 space plus 2 space e subscript 2

Answered by Sheetal Jalan | 12th Oct, 2014, 04:52: PM