The value of acceleration due to gravity decreases slightly with altitude above the Earth’s surface.
a. (i) Treating the Earth as a sphere of radius R and mass M, derive an expression for the acceleration due to gravity gh at a height h (with h≪R). Hence show that the fractional decrease in g is approximately 2h/R.
b. (ii) A pendulum that is a seconds pendulum at sea level has its time period increased to 2.006 s when taken to a hill station. Using your result of part (i) and neglecting any change in length, calculate the height of the station above sea level. Take R=6.4×106m.