Three students S 1 ,   S 2 and S 3 perform an experiment for determining the acceleration due to…

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 =0.1 m, least count for time =0.1 s)

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          .

Solution

T=2πgg=4π2T2
Δgg=Δ+2TT

ΔT= leastcountoftime ΔT0 numberofoscillations (n
Δgg=Δ+2ΔT0nT

As Δ and ΔT0 are same for all observations so
Δgg is minimum for highest value of , n and T

Minimum percentage error in g is for student number 1.

Asked in: JEE Main 2021 (22 Jul Shift 1)

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