Question

The radius of the moon is one-fourth, and its mass is one eighty-first that of the earth. If the acceleration due to gravity on the surface of the earth is 9.8 m/s2, what is its value on the moon’s surface.

Answer 1

given, $r_{moon}=\frac{1}{4}r_{earth}$

$M_{moon}=\frac{1}{81}M_{earth}$

given, acceleration due to gravity on the earth's surface is 9.8 m/s².

e.g., $g=\frac{GM_{earth}}{r_{earth}^2}$ = 9.8 m/s²

for moon,

acceleration due to gravity, $g' = \frac{GM_{moon}}{r_{moon}^2}$

= $\frac{16GM_{earth}}{81r_{earth}^2}$

= $\frac{16}{81}\frac{GM_{earth}}{r_{earth}^2}$

= $\frac{16}{81}g$

= 16/81 × 9.8

= 1.93 m/s²

hence, acceleration due to gravity on the moon's surface is 1.93 m/s²