Physics

Problem

A body of mass

m

is raised to a height

h

above Earth’s surface, where

h \ll R

and

R

is Earth’s radius. a. (i) Derive an expression for the acceleration due to gravity

g_h

at the height

h

in terms of

g

and

R

. b. (ii) Hence obtain the ratio of the body’s weight at height

h

to its weight on the surface of Earth, keeping terms up to first order in

\dfrac{h}{R}

. c. (iii) Using your result, calculate the percentage decrease in the weight of a

10\,\text{kg}

body when it is raised to a height of

5\,\text{km}

. Take

R = 6400\,\text{km}

and

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

. d. (iv) Comment on whether the inertial mass of the body has changed during this process, giving a brief justification.