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JEE Advanced Model Paper 4 with solutions for online practice
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© examsnet.com
Question : 5
Total: 54
Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and record time for different number of oscillations. The observations are shown in thetable. Least count for time = 0.1 s, Least count for length = 0.1 cm
Student
Length of the pendulum (cm)
Number of oscillations (n)
Total time for (n) oscillations (s)
Time period
I
64.0
8
128.0
16.0
II
64.0
4
64.0
16.0
III
20.0
4
36.0
9.0
If
E
1
,
E
I
I
and
E
I
I
I
are the percentage errors in g . i.e.
(
Δ
g
g
×
100
)
for student I , II and III respectively.
E
I
= 0
E
I
is maximum
E
1
=
E
I
I
E
I
I
I
is maximum
Validate
Solution:
T = 2π
√
l
g
⇒ g =
4
π
2
l
T
2
therefore ,
Δ
g
g
=
Δ
l
l
+
2
Δ
T
T
For student I ,
E
I
=
Δ
g
g
100 =
(
0.1
64.0
+
2
×
0.1
64.0
)
× 100 =
5
16
% = 0.312 %
For student II ,
E
I
I
=
(
0.1
64
+
2
×
0.1
64.0
)
× 100 =
15
32
% = 0.469 %
For student II ,
E
I
I
I
=
(
0.1
20.0
+
2
×
0.1
36.0
)
× 100 =
19
8
% = 1.05 %
© examsnet.com
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