Question

The value of $g$ at a height of $100km$ from the surface of the Earth is nearly (Radius of the Earth $=$ 6400km) ($g$ on the surface of the Earth $=$ $9.8m/s^2$)

• A. $9.5m{s}^{-2}$
• B. $8.5m{s}^{-2}$
• C. $10.5m{s}^{-2}$
• D. $9.8m{s}^{-2}$

Answer 1

The correct option is A $9.5m{s}^{-2}$

Acceleration due to gravity changes with the height from Earth's surface as:
$g^{{}^{\prime }}=g(1-\frac{2h}{R})$
$\Rightarrow g^{{}^{\prime }}=9.8(1-\frac{2\times 100}{6400})$
$\Rightarrow g^{{}^{\prime }}=9.8(1-\frac{1}{32})=9.49m/s^2$