Find the value of acceleration due to gravity on the surface of the moon, if its radius is `(1)/(4)th` of the radius of the earth and mass is `1/(96)th` the mass of earth.

Explanation

We are given: Radius of moon `(R_("moon"))= (R_(e ))/(4)`
Mass of moon `(M_("moon")) = (M_(e ))/(96)`
We are to calculate, Acceleration due to gravity at moon `(g_("moon"))` using relation,
`g_("earth")= (GM_(e))/(R_(e)^(2)) rArr g_("moon") = (GM_("moon"))/(R_("moon")^(2))`
So `g_("moon")= (G xx M)/(96 xx R_(e)^(2)) xx 16= (1)/(6) (GM_(e ))/(R_(e)^(2))`
As `(GM_(e))/(R_(e)^(2)) = g_("earth"), " so " g_("moon") = (g_("earth"))/(6)`. Hence, `g_("moon")=(g_("earth"))/(6)`