Physics

Problem

A body of mass

10\,\text{kg}

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 = 9.8\,\text{m s}^{-2}

and

R = 6.4\times10^{6}\,\text{m}

.) a. (i) Write an expression for the weight of the body at the Earth’s surface. b. (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

. c. (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. d. (iv) Repeat the percentage‐decrease calculation using the approximate relation

g_h = g\bigl(1-2h/R\bigr)

. Compare the two answers and state which one is more accurate for

h = 0.20R

, giving a brief reason.

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