Physics

Problem

An object of mass

m

is taken from the Earth’s surface to a height

h

such that

h \ll R

, where

R

is the Earth’s radius. (i) Using the approximate expression

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

, derive an expression for the fractional change in the weight of the object. (ii) Hence obtain the percentage decrease in weight in terms of

h

and

R

. (iii) Calculate the height above the Earth’s surface at which the weight of the object decreases by

1\%

. Take

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

. a. (i) Using the relation

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

, derive an expression for the fractional change in the weight of the object. c. (iii) Calculate the height above the Earth’s surface at which the weight of the object decreases by

1\%

, taking

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

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