An experimental balloon carrying instruments rises vertically from sea level to a…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

An experimental balloon carrying instruments rises vertically from sea level to a height of

10.0\,\text{km}

. (i) Using the exact expression for the variation of

g

with altitude, calculate the percentage decrease in

g

between the ground and the balloon’s final position. Take

R_E = 6.4 \times 10^6\,\text{m}

and

g = 9.80\,\text{m\,s}^{-2}

. (ii) Obtain the same percentage decrease by employing the small-altitude approximation valid for

h \ll R_E

. (iii) Compare the two results and comment on the validity of the small-altitude approximation at

10\,\text{km}