Calculating Period of Rotation for Mars-Bound Weight at 3.8 m/s2

[HKfish]

Homework Statement

As a spacecraft of diameter 2.8km approaches Mars, the astronauts want to experience what their Mars-bound weight will be. What should the period of rotation be to simulate an acceleration due to gravity of magnitude 3.8 m/s² ?

Mass of Mars = 6.37*10²³
Radius of Mars = 3.40*10⁶

Homework Equations

(1) F_g = (GMm)/r²

(2) a_c = (mv²)/r

(3) T = (2∏r)/v

The Attempt at a Solution

F_g = a_c
(GMm)/r² = (mv²)/r

Solving for v
v = √((GM)/r)

Sub v into eqn. (3)
T = (2∏r)*(√(r)/√(GM))
T = (2∏r^(3/2))/√(GM)

And that's as far as i got cause I'm not sure what to do with the given information... The answer is 1.2*10²s.

 

[Dick]

You don't need to do anything with G or those mass figures. They already gave you the acceleration required. So the force produced will be F=ma=m*(3.8m/s^2). Equate that to mv^2/r.