Three students S₁, S₂ and S₂ 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)	No. of oscillations (n)	Total 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 cm

least count for time = 0.1 s)

If E₁, E₂ and E₃ are the percentage errors ‘g’ for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no.___________.

<p><span contenteditable="false"> <math> <mrow> <mi>T</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi mathvariant="script">l</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mi>g</mi> <mo>=</mo> <mn>4</mn> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mfrac> <mrow> <mi mathvariant="script">l</mi> </mrow> <mrow> <msup> <mrow> <mi>T</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mfrac> <mrow> <mi>Δ</mi> <mi>g</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>Δ</mi> <mi mathvariant="script">l</mi> </mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>Δ</mi> <mi>T</mi> </mrow> <mrow> <mi>T</mi> </mrow> </mfrac> </mrow> </math> </span></p><p>Student 1 will get least error because it has more number of oscillation</p>

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