Problem 1.3: The length of a pendulum is (100 ± 0.1) cm. If the acceleration of the free fall is (9.8 ± 0.1) m/s2, calculate the percentage uncertainty in the time period of the pendulum.
Solution
Given: Length of the pendulum = (100 ± 0.1) cm
Acceleration due to gravity = (8.9 ± 0.1) cm
Required: T o find the Percentage uncertainty in the time period of the pendulum.
Strategy
- Time period of a pendulum is, T = 2π(l/g)1/2 .
- Quotient rule for percentage uncertainty is Δx = ±(Δy + Δz) .
- Rule for percentage uncertainty in power is “multiply the percentage uncertainty with the power in the final result”.
Now the percentage uncertainty in length ‘l’ is
![](https://mashalscienceacademy.com/wp-content/uploads/2020/11/p11c1nume8.png)
Percentage uncertainty in ‘g’ is
![](https://mashalscienceacademy.com/wp-content/uploads/2020/11/p11c1nume9.png)
Use quotient rule to find percentage uncertainty in l/g.
Percentage uncertainty in l/g = ±(0.1 + 1.02) = ±1.12
Use the formula for time period ‘T’ and power rule to find the percentage uncertainty in the time period.
Percentage uncertainty in time period
![](https://mashalscienceacademy.com/wp-content/uploads/2020/11/p11c1nume10.png)
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