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IIT JEE Advanced 2010 Paper 1
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© examsnet.com
Question : 11
Total: 84
A student uses a simple pendulum of exactly 1 m length to determine g, the acceleration due to gravity. He uses a stopwatch with the least count of 1 s for this and records 40 s for 20 oscillations. For this observation, which of the following statement(s) is(are) true?
Error ΔT in measuring T, the time period, is 0.05 s.
Error ΔT in measuring T, the time period, is 1 s.
Percentage error in the determination of g is 5%.
Percentage error in the determination of g is 2.5%.
Validate
Solution:
We have
g =
4
π
2
l
t
2
⇒
Δ
g
g
=
Δ
l
l
+
2
Δ
t
t
Δ
t
t
=
1
40
= 0.25 (Since Δl = 0)
Therefore,
Δt = 0.025 × 2 = 0.05 s
So, the error in measurement is
Δ
g
g
=
2
Δ
T
T
= 2 ×
0.05
2
The percentage error in measurement of g is 5%.
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