An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :

Question

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :, 4.4%, 2.27%, 1.7%, 2.7%

MARKS App · Accepted Answer

T = 2 π L g ∴ T 2 = 4 π 2 L g ∴ g = 4 π 2 L T 2 % Error in g = Δ L L 0 × 1 0 0 + 2 Δ T T 0 × 1 0 0 = 1 × 1 0 - 3 0.20 × 1 0 0 + 2 1 9 0 × 1 0 0 = 0.5 + 2 1 0 9 = 0.5 + 2 0 9 = 0.5 + 2.22 = 2.7%

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