The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity

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Solution

Q.
The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is: [2024]

1 4

2 8

3 6

4 5

Ans.
(3)

$T = 2 π \sqrt{\frac{l}{g}}$

   $g = \frac{4 π^{2} l}{T^{2}}$

   $\frac{∆ g}{g} = \frac{∆ l}{l} + \frac{2 ∆ T}{T} = \frac{0.2}{20} + 2 (\frac{1}{40}) = \frac{1.2}{20}$

Percentage change = $\frac{1.2}{20} \times 100 = 6 %$

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