Question

Suppose a pendulum clock has been calibrated to be accurate in San Francisco, where g = 9.800 m/s2 . In Camrose, g = 9.811 m/s2 is slightly larger due to the effect of Earth’s rotation at a higher latitude. Explain why the clock will either run perfectly, run too quickly, or run too slowly in Camrose.

Answer 1

The clock would run too slowly in Camrose.

Since the period of the pendulum T = 2π√(L/g) where L = length of clock and g = acceleration due to gravity.

Now since g = 9.800 m/s² in San Francisco and g = 9.811 m/s² in Camrose, we see that g increases.

From the expression for the period T, since L is constant, we find that

T ∝ 1/√g

Since g increases, so, T would decrease.

Thus, the clock would run too slowly in Camrose.

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