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JEE Main 2021 — Mathematics in Physics Question with Solution

JEE Main 2021 (22 Jul Shift 1)

Question

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          .

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Show full solutionCorrect answer: 1
Correct answer
1

Step-by-step explanation

T=2πℓg⇒g=4π2ℓT2
Δgg=Δℓℓ+2∆TT

ΔT= leastcountoftime ΔT0 numberofoscillations (n) 
Δgg=Δℓℓ+2ΔT0nT

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

⇒ Minimum percentage error in g is for student number 1.

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About this question

This is a previous-year question from JEE Main 2021, covering the Mathematics in Physics chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.