A simple pendulum keeps accurate time at a physics laboratory situated at sea level where the acceleration due to gravity is 9.80m s−2. The same pendulum is later taken to an observatory located on a hill top where the local value of g is 9.76m s−2.
(a) Without performing any numerical calculation, state whether the time period of the pendulum will increase, decrease, or remain unchanged at the hill top. Give a concise reason for your answer.
(b) Show that the ratio of the new time period Thill to the original time period Tsea can be expressed as 9.769.80.
(c) A pendulum clock based on this bob is carried to the hill top and allowed to run for 24h according to its own dial. Will the clock gain time, lose time, or remain correct relative to a standard clock kept at sea level? Justify quantitatively without converting the square-root expression into a decimal.