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, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e 1 and e 2 respectively, the percentage error in the estimation of g is
Text Solution
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From the relation
h = ut + 
gt 2 h = 
gt
2 ⇒ g = 
( body initially at rest)
Taking natural logarithm on both sides, we get
λ ng = λ n h – 2 λ n t
Differentiating, 
For maximum permissible error,
or 
According to problem
= e 1 and 
= e 2
Therefore, 
= e 1 + 2e 2
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