A person moves to the city of Oslo ( g= 9.825 ms-2 ) from Singapore ( g= 9.780 ms-2 ). He observes that the time period of his pendulum clock has changed after he reached Oslo. He goes to a mechanic and the mechanic increased the length of the pendulum to adjust the time period. Suggest a possible explanation to this case using the results of the investigation.
Question
A person moves to the city of Oslo ( g= 9.825 ms-2 ) from Singapore ( g= 9.780 ms-2 ). He observes that the time period of his pendulum clock has changed after he reached Oslo. He goes to a mechanic and the mechanic increased the length of the pendulum to adjust the time period. Suggest a possible explanation to this case using the results of the investigation.
Solution
The time period of a pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
In Singapore, the value of g is 9.780 ms-2, and in Oslo, it is 9.825 ms-2. The increase in the value of g in Oslo means that the pendulum would swing faster, thus decreasing the time period of the clock.
To compensate for this change and to make the clock show the correct time, the mechanic would need to increase the length of the pendulum. This is because the time period is directly proportional to the square root of the length of the pendulum. By increasing the length of the pendulum, the time period would increase, thus compensating for the increased value of g in Oslo.
Therefore, the change in the time period of the pendulum clock when moving from Singapore to Oslo can be explained by the change in the value of the acceleration due to gravity, and the adjustment made by the mechanic is consistent with the mathematical relationship between the time period, the length of the pendulum, and the acceleration due to gravity.
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