what is the acceleration due to gravity and radius

Question

An astronaut drops a penny on Mercury from a height of 2.6 meters. It takes 3.1 seconds to drop to the ground. 

a. What is the acceleration due to gravity on Mercury?

b. If the mass of mercury is 7.158 x 10^24, what must its radius be?

Answer 1

Use the kinematic equation, x=x₀ + vt + (1/g)gt² to find g

Applying v=0, x₀=0, g = 2x/t²

g on the surface mercury :

According to Newton's law of gravitation, the force on a mass m is GMm/r² ,

where G = unviersal gravitational constat

M mass of mercury

r = radius of Mercury

mg = GMm/r² ,

r = √(GM/g) Now plug in the values to get the radius