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

Step-by-step solution

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.