Question

Acceleration due to gravity at earth's surface is '$g$' m/s${}^2$. Find the effective value of acceleration due to gravity at a height of $32km$ from sea level :($R_e=6400km$).

• A. $0.5gm{s}^2$
• B. $0.99gm{s}^2$
• C. $1.01gm{s}^2$
• D. $0.90gm{s}^2$

Answer 1

Answer: (B)

$0.99gm{s}^2$

Acceleration due to gravity at a height h from the earth surface, $g^{\prime }=g[1+\frac{h}{R}{]}^{-2}$

Given $h=32kmR=6400km$

Using bionomial expansion, $(1+x{)}^n=1+nx$ for $x<<1$

Thus as $h<<R$ $⟹g^{\prime }=g[1-\frac{2h}{R}]$

$g^{\prime }=g[1-\frac{2\left(32\right)}{6400}]$

$⟹g^{\prime }=.99gm/s^2$