Errors in measurementMedium
Question
A student measure the distance traversed in free 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 time are e1 and e2 respectively, the percentage error in estimation of g is
Options
A.e2 - e1
B.e1 + 2e2
C.e1 + e2
D.e1 - 2e2
Solution
From the relation
h = ut +
gt2
h =gt2 ⇒ g = 
(∵ body initially at rest)
Taking natural logarithm on both sides, we get
ln g = ln h - 2ln t
Differentiating,
For maximum permissible error,
or
According to problem
× 100 = e1 and 
× 100 = e2
Therefore,
= e1 + 2e2
h = ut +
gt2h =
gt2 ⇒ g = (∵ body initially at rest)Taking natural logarithm on both sides, we get
ln g = ln h - 2ln t
Differentiating,
For maximum permissible error,
or
According to problem
× 100 = e1 and × 100 = e2 Therefore,
= e1 + 2e2 Create a free account to view solution
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