A pendulum clock keeps correct time at sea level where the acceleration due to gravity is 9.80m s−2. When the clock is taken to a hill station it is found to lose 12.0s every hour.
(i) Derive an expression that relates the fractional change in the time period TΔT to the fractional change in the acceleration due to gravity gΔg for small variations.
(ii) Using the result of part (i), calculate the value of g at the hill station.
(iii) Without changing location, the clock can be corrected by adjusting the length of its pendulum. By what percentage should the length be altered? State clearly whether it has to be increased or decreased.