Question

Find the free-fall acceleration of an object on the surface of the moon, if the radius of the moon and its mass are $1740km$ and $7.4\times {10}^{22}$ kg respectively. Take $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

• A. $1.63m{s}^{-2}$
• B. $1.83m{s}^{-2}$
• C. $9.8m{s}^{-2}$
• D. $10m{s}^{-2}$

Answer 1

The correct option is A $1.63m{s}^{-2}$

Given:
Mass of the moon, $M=7.4\times {10}^{22}kg$
Radius of moon, $R=1740\times {10}^{3}m$
Gravitational constant, $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Acceleration of gravity near Moon's surface is given by:
$g_m=\frac{GM}{R^2}$
$g_m=\frac{6.67\times {10}^{-11}\times 7.4\times {10}^{22}}{{(1740\times {10}^3)}^2}$
$g_m\approx 1.63m{s}^{-2}$