A pendulum clock that gives correct time at a location where g = 9.800 m/s ^2 is transported to a new location, where it is observed to lose 24 seconds over a period of 24 hours. Determine the value of g at this new location.

Step-by-step solution

The time period of a simple pendulum is given by T = 2 l g . Taking the natural logarithm and differentiating, we get the fractional change in the time period: T T = - 1 2 g g The time lost by the clock in a total time t is given by t = t T T . Given that the clock loses 24 seconds in 24 hours ( 86400 seconds), the fractional change in the time period is: T T = 24 86400 = 1 3600 Substituting this into the fractional change equation: 1 3600 = - 1 2 g g g = -g 2 3600 = -9.800 1 1800 -0.00544 m/s ^2 The acceleration d