Question

Calculate the percentage error in the determination of g by using a simple pendulum if the length l and time period T are measured with ±2% and ± 3% errors respectively​

Answer 1

Answer: 2.5%

Explanation:

we know the time period of simple pendulam. which is, T = 2π√(l/g)

=> ΔT /T = √Δl/l + √Δg/g

=> ΔT /T * 100 = 1/2 (Δl/l * 100) + 1/2 (Δg/g * 100)

=> % age error in T  = 1/2 (% age error in l) + 1/2(% age error in  g)

=> % age error in T = 1/2 *2 + 3/2

=> % age error in T = 1 + 3/2 = 2.5 %

NOTE : we can only apply this method if error are small [i.e less than 7%]

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Amrit