Question

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

Answer 1

moon's gravity is 4/25 times that of the earth

Answer 2

Given that,

If mass of moon is 1 /100th the mass of earth and radius of moon is 1/ 4th radius of earth.

To find,

The ratio of acceleration due to gravity on earth to that on the moon.

Solution,

$M_M=\dfrac{M_E}{100}\\\\r_M=\dfrac{r_E}{4}$

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

$g_E=\dfrac{GM_E}{r_E^2}$ ......(1)

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

$g_M=\dfrac{GM_M}{r_M^2}$  .......(2)

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

$\dfrac{g_E}{g_M}=\dfrac{\dfrac{GM_E}{r_E^2}}{\dfrac{GM_M}{r_M^2}}$

$\dfrac{g_E}{g_M}=\dfrac{M_Er_M^2}{M_Mr_E^2}}\\\\\dfrac{g_E}{g_M}=\dfrac{M_E}{r_E^2}\times (\dfrac{r_E}{4})^2\times \dfrac{100}{M_E}\\\\\dfrac{g_E}{g_M}=\dfrac{100}{16}\\\\\dfrac{g_E}{g_M}=\dfrac{25}{4}$

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

Learn more,

Acceleration due to gravity

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