A simple pendulum of length 1.00m has a period T0 at the Earth’s surface. The pendulum is taken down a vertical mine that is 800m deep. Assume the Earth to be of uniform density with radius R=6.4×106m and surface acceleration due to gravity g=9.8ms−2.
(i) Calculate the value of g at the bottom of the mine.
(ii) Determine the period of the pendulum at that depth.
(iii) By what percentage has the period increased compared with T0? Give your answer correct to two significant figures.