If the mass of the moon is 1/100 th the mass of the earth and the radius of moon is 1/4th to the radius of earth , what is the ratio of acceleration due to gravity on earth to that on the moon?


Given: The mass of moon is 1/100 th the mass of the earth and the radius of moon is 1/4th to the radius of earth

To find: the ratio of acceleration due to gravity on earth to that on the moon 

Solution:

Let $m = \frac{1}{100} \times M$ and $ r = \frac{1}{4} \times R$

The acceleration due to gravity on the surface of Earth is given by :

 $g_{e} = \frac{GM}{R^2}$......(1)

Acceleration due to gravity on the moon's surface is :

 $g_{m} = \frac{Gm}{r^2}$......(1)

Dividing equation (1) and (2) and put initial condition,

$\frac{g_{e}}{g_{m}} =\frac{ GM/R^2 }{  Gm/r^2}$

$=  \frac{GM/R^2  }{  G(M/100) \div (R/4)^2}$

                                                     

$= \frac{100}{16} = \frac{25}{4}$

$ \frac{g_{e}}{g_{m}}= \frac{25}{4}$

So, the ratio of acceleration due to gravity on earth to that on the moon is 25:4.


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Updated on: 10-Oct-2022

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