Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity at a height $h$ above the surface of the earth, where $h\ll R$, is given by

$g^{\prime }=g\left(1-\frac{2h}{R}\right)$

The fractional decrease in weight is

$\frac{\Delta W}{W}=\frac{g-g^{\prime }}{g}=\frac{2h}{R}$

The percentage decrease in weight is

$\frac{\Delta W}{W}\times 100=\frac{2h}{R}\times 100$

Substituting $h=48$ km and $R=6400$ km:

Percentage decrease $=\frac{2\times 48}{6400}\times 100$

Percentage decrease $=\frac{96}{64}=1.5\%$

Answer: $1.5\%$