The time period of oscillation of a simple pendulum is given by T = 2 π l g . The length of the pendulum is measured as l = 10 ± 0.01 c m and the time period as T = 0.5 ± 0.02 s . The percentage error

Question

The time period of oscillation of a simple pendulum is given by T = 2 π l g . The length of the pendulum is measured as l = 10 ± 0.01 c m and the time period as T = 0.5 ± 0.02 s . The percentage error in the value of g is

TestHub · Accepted Answer

Δ g g × 100 = Δ l l × 100 + 2 Δ T T × 100 Δ l = 0.01 c m Δ T = 0.02 s l = 10 c m T = 0.5 s Δ l l × 100 = 0.01 10 × 100 = 0.1 Δ T T × 100 = 0.02 0.5 × 100 = 4 Δg g × 100 = 0.1 + 2 × 4 ≈ 8 %

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