Answer
$z = 8862 m$
Work Step by Step
The variation of gravitational acceleration above the sea level is given as a function of altitude. The height at which the weight of a body will decrease by 0.3% is to be determined.
The weight of a body at the elevation z can be expressed as
$W = mg = m(9.807-3.32\times10^{-6}z)$
In our case,
$W = (1 - 0.3/100)W_s = 0.997W_s = 0.997mg_s = 0.997(m)(9.807)$
Substituting,
$0.997(9.807) = (9.807-3.32\times10^{-6}z)$
$z = 8862 m$
