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JEE Advanced 2017 Paper 2
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© examsnet.com
Question : 6
Total: 54
A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is
δ
=
T
0.01
seconds and he measures the depth of the well to be L = 20 meters. Take the acceleration due to gravity
g
=
10
m
s
−
2
and the velocity of sound is
300
m
s
−
1
Then the fractional error in the measurement,
δ
L
L
, is closet to :
0.2%
5%
1%
3%
Validate
Solution:
Time taken for the stone to reach the bottom of the well.
t
1
=
√
2
L
g
time taken by the sound to reach from the bottom of the well to the observer
t
2
=
L
V
s
Total time
T
=
t
1
+
t
2
⇒
T
=
√
2
L
g
+
L
V
s
d
T
d
L
=
−
1
2
√
2
g
×
1
√
L
+
1
V
s
=
1
2
×
√
2
10
×
20
+
1
300
=
1
20
+
1
300
0.01
d
L
=
15
+
1
300
⇒
d
l
=
0.01
×
300
16
=
3
16
Percentage error,
d
l
l
×
100
=
3
16
×
1
20
×
100
≈
1
%
© examsnet.com
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