Question

An exoplanet has three times the mass and one-fourth the radius of the Earth. Find the acceleration due to gravity on its surface, in terms of g, the acceleration of gravity at Earth's surface. A planet's gravitational acceleration is given by gp = G Mp/r^2p

a. 12.0 g.
b. 48.0 g.
c. 6.00 g.
d. 96.0 g.
e. 24.0 g.

Answer 1

b. 48.0 g.

Step-by-step explanation:

Given;

mass of the exoplanet,
`M_p = 3M_e`

radius of the exoplanet,
`r_p = (1)/(4) r_e`

The acceleration due to gravity of the planet is calculated as;

`g_p = (GM_p)/(r_p^2) \\\\for \ Earth's \ surface\\\\g = (GM_e)/(r_e^2) \\\\G = (gr_e^2)/(M_e) = (g_pr_p^2)/(M_p) \\\\(gr_e^2)/(M_e) = (g_p((r_e)/(4)) ^2)/(3M_e) \\\\(gr_e^2)/(M_e) = (g_pr_e ^2)/(16* 3M_e) \\\\g = (g_p)/(48) \\\\g_p = 48 \ g`

Therefore, the correct option is b. 48.0 g