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 lengths of pendulum and record time for differe

Question

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 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 E 1 , E 2 and E 3 are the percentage errors in g for students 1 , 2 and 3 , respectively, then the minimum percentage error is obtained by student no .

TestHub · Accepted Answer

T = 2 π ℓ g ⇒ g = 4 π 2 ℓ T 2 Δ g g = Δ ℓ ℓ + 2 ∆ T T Δ T = l e a s t count of time Δ T 0 n u m b e r of oscillations ( n ) Δ g g = Δ ℓ ℓ + 2 Δ T 0 n T As Δ ℓ and Δ T 0 are same for all observations so Δ g g is minimum for highest value of ℓ , n and T ⇒ Minimum percentage error in g is for student number 1.

Student No.	Length of pendulum $(cm)$	Number of oscillations $(n)$	Total time for $n$ oscillations	Time period $(s)$
$1 .$	$64.0$	$8$	$128.0$	$16.0$
$2 .$	$64.0$	$4$	$64.0$	$16.0$
$3 .$	$20.0$	$4$	$36.0$	$9.0$

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