A miner notices that his true weight recorded by a precision spring balance increases by 0.50% when he descends vertically from the surface to the bottom of a shaft.
(i) Establish the mathematical relation connecting the fractional change in weight and the depth reached (depth ≪ Earth’s radius).
(ii) Using g=9.8ms−2 at the surface and R=6.4×106m, determine the depth of the shaft in metres, correct to two significant figures.
(iii) The miner’s mass is 70kg. Calculate his weight at the bottom of the shaft.
(iv) State clearly whether his mass has changed and give a brief reason.