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# How would the period of vibration be changed if the gravitational acceleration were increased by 5%?

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12 years ago
 How would the period of vibration be changed if the gravitational acceleration were increased by 5%? How would the period of vibration be changed if the gravitational acceleration were increased by 5%?? Read 843 times 1 Reply

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Anonymous
wrote...
3 months ago
 The period of vibration of a pendulum is affected by the gravitational acceleration, among other factors. The period of a pendulum (T) is given by the formula:$T = 2π \sqrt{\frac{L}{g}}$Where:- $$T$$ = period of the pendulum- $$L$$ = length of the pendulum- $$g$$ = acceleration due to gravityIf the gravitational acceleration were increased by 5%, it means $$g$$ becomes $$1.05g$$ (where $$g$$ is the original value of the gravitational acceleration). Let's denote the original period of vibration as $$T_{\text{original}}$$ and the new period as $$T_{\text{new}}$$. We can set up a ratio of the new period to the original period:$\frac{T_{\text{new}}}{T_{\text{original}}} = \sqrt{\frac{g_{\text{original}}}{g_{\text{new}}}}$Substituting $$g_{\text{new}} = 1.05g$$ and $$g_{\text{original}} = g$$:$\frac{T_{\text{new}}}{T_{\text{original}}} = \sqrt{\frac{g}{1.05g}} = \sqrt{\frac{1}{1.05}}$To find the percentage change in the period of vibration, we can compute:$\text{Percentage Change} = \left(1 - \frac{T_{\text{new}}}{T_{\text{original}}}\right) \times 100\%$Let's calculate this percentage change. Assuming $$g = 9.8 \, \text{m/s}^2$$ (standard acceleration due to gravity):$\frac{T_{\text{new}}}{T_{\text{original}}} = \sqrt{\frac{1}{1.05}} \approx 0.9971$$\text{Percentage Change} = \left(1 - 0.9971\right) \times 100\% \approx 0.29\%$So, increasing the gravitational acceleration by 5% would decrease the period of vibration of the pendulum by approximately 0.29%.