In an experiment to determine the value of acceleration due to gravity g using a simple pendulum , the measured value of lenth of the pendulum is 31.4 cm known to 1 mm accuracy and the time period for 100 oscillations of pendulum is 112.0 s known to 0.01 s accuracy . find the accuracy in determining the value of g.

Explanation

To determine the accuracy in calculating the value of acceleration due to gravity \( g \) using the given measurements, we will follow these steps:

### Step 1: Identify the given values
- Length of the pendulum, \( L = 31.4 \, \text{cm} = 31.4 \times 10^{-2} \, \text{m} \)
- Accuracy in length measurement, \( \Delta L = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Time period for 100 oscillations, \( T_{100} = 112.0 \, \text{s} \)
- Accuracy in time measurement, \( \Delta T = 0.01 \, \text{s} \)

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