Find the free-fall acceleration of an object on the surface of the moon, if the radius of the moon and its mass are 1740 km and 7.4 x 1022 kg respectively. Compare this value with free-fall acceleration of a body on the surface of the earth.

According to the question given data is;

Mass of the moon (M) = 7.4 x 10²² Kg;

Radius of moon (R) = 1740 km = 1740 x 10³ m (1km = 1000m).

Now;

Acceleration due to gravity (g) =

⇒ g =

⇒ g =

⇒ g =

⇒ g =

⇒ g =

⇒ g = 1.63 ms².

Free fall Acceleration at the surface of the moon is 1.63 ms²

Now;

Acceleration due to gravity on earth ag_e = 9.8 ms² .

Acceleration due to gravity on moon g_m = 1.63 ms² .

⇒

g_e = 6 g_m.

Acceleration due to gravity on the moon is one-sixth of Acceleration due to gravity on earth.