Physics

Problem

1.0\times10^{3}\,\text{kg}

scientific probe is lifted slowly from Earth’s surface to an altitude of 100\,km. A student who assumes

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

throughout obtains

\Delta U_{\text{const}}=9.8\times10^{8}\,\text{J}

. Given

R_E=6.37\times10^{6}\,\text{m}

and

g_0=9.8\,\text{m/s}^2

, which of the following best describes the accuracy of this constant-

g

estimate relative to the exact value found from the inverse-square law? a) It is too small by roughly

1.5\%

. b) It is too large by roughly

1.5\%

. c) It is accurate to within

0.2\%

. d) It is too large by roughly

15\%