The period of oscillation of a simple pendulum is . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch of 1s resolution. The accuracy in the determination of g is :math widget

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Physics

SHM of Simple Pendulum

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The period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch of 1s resolution. The accuracy in the determination of g is :

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$\frac{Δg}{g} = \frac{Δℓ}{ℓ} + \frac{2 ΔT}{T}$

$= \frac{1 \times 100}{200} + \frac{2 \times 1}{90} \times 100$

$= \frac{1}{2} + \frac{20}{9} = \frac{9 + 40}{18} = \frac{49}{18} = 3 %$