Students I, II and III perform an experiment for measuring the acceleration due to gravity ( g ) using a simple pendulum. They use different lengths of the pendulum and/or record time for different nu

Question

Students I, II and III perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table. Least count for length $= 0.1 cm$ Least count for time $= 0.1 s$
If $E_{I}, E_{II}$ and $E_{III}$ are the percentage errors in $g$ , i.e., $(\frac{Δ g}{g} \times 100)$ for students I, II and III, respectively.

TestHub · Accepted Answer

∴ ​ T g ​ = 2 π g l ​ ​ or n t ​ = 2 π g l ​ ​ = t 2 ( 4 π 2 ) ( n 2 ) l ​ ​ % error in g = g Δ g ​ × 100 = ( l Δ l ​ + t 2 ⋅ Δ t ​ ) × 100 ​ E I ​ = ( 64 0.1 ​ + 128 2 × 0.1 ​ ) × 100 = 0.3125% E II ​ = ( 64 0.1 ​ + 64 2 × 0.1 ​ ) × 100 = 0.46875% E III ​ = ( 20 0.1 ​ + 36 2 × 0.1 ​ ) × 100 = 1.055% ​ Hence, E I ​ is minimum. ∴ correct option is (b).

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