A meteorological research balloon rises vertically from sea level.
(i) Calculate the value of acceleration due to gravity at an altitude of 8 km. Take Earth’s radius R = 6.4×10⁶ m and g at sea level as 9.80 m s⁻².
(ii) Determine the percentage decrease in g at this altitude compared with the surface value.
(iii) If the same balloon were lowered instead into a mine shaft to a depth of 4 km below sea level, calculate the value of g there and state the corresponding percentage change relative to the surface.