Three students S_1,S_2 and S_3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different…
JEE Main 2021 — Physics Mechanics
2021integermedium
Three students S1,S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
Student No.
Length of pendulum (cm)
Number of oscillations (n)
Total time for n oscillations
Time period (s)
1.
64.0
8
128.0
16.0
2.
64.0
4
64.0
16.0
3.
20.0
4
36.0
9.0
(Least count of length =0.1m, least count for time =0.1s)
If E1,E2 and E3 are the percentage errors in g for students 1,2 and 3, respectively, then the minimum percentage error is obtained by student no .
Official previous-year question
Held on 22 Jul 2021 · Verified 6 Jul 2026.
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Solution
T=2πgℓ⇒g=T24π2ℓ
gΔg=ℓΔℓ+T2ΔT
ΔT=numberofoscillations(n)leastcountoftime(ΔT0)
gΔg=ℓΔℓ+nT2ΔT0
As Δℓ and ΔT0 are same for all observations so
gΔg is minimum for highest value of ℓ,n and T
⇒ Minimum percentage error in g is for student number 1.
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