The moon's radius is `1//4` that of the earth and its mass is `1//80` times that of the earth. If g represents the
acceleration due to gravity on the surface of the earth, that on the surface of the moon is

Options

A. `(g)/(4)`
B. `(g)/(5)`
C. `(g)/(6)`
D. `(g)/(8)`

Answer

B

Explanation

Acceleration due to gravity g = `("GM")/(R^(2))`
`therefore (g_("moon"))/(g_("earth"))=(M_("moon"))/(M_("earth")).(R_("earth")^(2))/(R_("moon"^(2)))=(1/(80))(4/1)^(2)`
`g_("moon")=g_("earth") xx (16)/(80)=(g)/(5)`