A body of mass is first taken to a small height above Earth’s surface and later…
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A body of mass m is first taken to a small height h above Earth’s surface and later lowered to a small depth d below the surface. Assume h,RmE,d satisfy h≪RE and d≪RE.
(i) Write the expression for the acceleration due to gravity at an altitude h and hence obtain the exact expression for its weight Wh.
(ii) Using the first–order binomial approximation, derive an expression for the fractional change in weight W0Wh−W0, where W0 is the weight at the surface.
(iii) Write the corresponding exact expression for the acceleration due to gravity at a depth d and hence obtain Wd.
(iv) Using a first–order approximation, derive W0Wd−W0.
(v) Explain physically why the weight keeps decreasing on moving away from the surface both upward and downward, and state what happens to the weight at the centre of Earth.