Question

Calculate acceleration due to gravity at a height of $2000km$ above the Earth's surface. Mass of Earth = $6\times {10}^{24}kg$, radius of Earth = $6.4\times {10}^6$ m and (Gravitational constant, G $=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$)

• A. $4.7m{s}^{-2}$
• B. $5.7m{s}^{-2}$
• C. $3.7m{s}^{-2}$
• D. $6.7m{s}^{-2}$

Answer 1

The correct option is B

$5.7m{s}^{-2}$

Given,
mass of the Earth, $M_e=6\times {10}^{24}kg$,
radius of the Earth,$R_e=6.4\times {10}^{6}m$,
height above the earth's surface, $h=2000\times {10}^{3}m$ and $G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$.

When the body is at height $h$ above the surface of the earth then the distance of the body from the centre of the Earth will be $R=R_e+h$.

So, $R=6.4\times {10}^6+2000\times {10}^3$
$=8.4\times {10}^{6}m$

Since, acceleration due to gravity, $g=\frac{GM}{R^2}$

So, $g=\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}}{{(8.4\times {10}^6)}^2}$

On solving we get $g=5.7m{s}^{-2}$.