A body of mass 10kg is lifted from the Earth’s surface to an altitude h=0.20R, where R is the mean radius of the Earth.
Answer the following questions. (Take g=9.8m s−2 and R=6.4×106m.)
(i) Write an expression for the weight of the body at the Earth’s surface.
(ii) Obtain, without using any series approximation, an exact expression for the weight of the body at a height h in terms of g, R, and h.
(iii) Using your expression from part (ii), calculate the numerical value of the weight of the body at h=0.20R and hence find the percentage decrease in weight compared with its surface value.
(iv) Repeat the percentage‐decrease calculation using the approximate relation gh=g(1−2h/R). Compare the two answers and state which one is more accurate for h=0.20R, giving a brief reason.