Question

At what height above the surface of earth the value of ${}^{\prime \prime }{g}^{\prime \prime }$ decreases by $2\%$ ? [radius of the earth is $6400km$ ]

• A. 32 km
• B. 64 km
• C. 128 km
• D. 1600 km

Answer 1

Answer: (B)

Acceleration due to gravity above the surface of earth at a height $h$ is given $g^{\prime }=g\left(1-\frac{2h}{R_{\theta }}\right)$
here, $g^{\prime }=0.98g$
$\Rightarrow 0.98=1-\frac{2h}{R_e}$
$\Rightarrow \frac{2h}{R_e}=0.02$
$h=0.01R_e$
$=0.01\times 6400km$
$=64km$