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 earth surface is 9.8 m/s² ,what is the value on the moon 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

Answer 2

Explanation:hope it is helpful

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