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Test Index
Class 11 NEET Physics Physical World, Units and Measurements
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© examsnet.com
Question : 34
Total: 67
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
(2010 Mains)
e
2
−
e
1
e
1
+
2
e
2
e
1
+
e
2
e
1
−
2
e
2
Validate
Solution:
From the relation
h
=
u
t
+
1
2
g
t
2
,
h
=
1
2
g
t
2
⇒
g
=
2
h
t
2
(∵ body initially at rest)
Taking natural logarithm on both sides,we get
l
n
g
=
l
n
2
+
l
n
h
−
2
l
n
t
Differentiating,
Δ
g
g
=
Δ
h
h
−
2
Δ
t
t
For maximum permissible error,
or
(
Δ
g
g
×
100
)
m
a
x
=
(
Δ
h
h
×
100
)
+
2
×
(
Δ
t
t
×
100
)
According to problem
Δ
h
h
×
100
=
e
1
and
Δ
t
t
×
100
=
e
2
Therefore,
(
Δ
g
g
×
100
)
m
a
x
=
e
1
+
2
e
2
© examsnet.com
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