Answer:
11.67 revolutions per minute
Explanation:
Centripetal acceleration a  =  r ω ²
Where, ω  is angular velocity.
From the question, centripetal acceleration equal to that of the earth’s gravity
                   g  =  r ω ²
substituting the values of acceleration due to gravity g and radius r                   Â
                  9.8 = 2.30 x ω ²
                  ω ² = [tex]\frac{9.8}{2.30}[/tex]
                  ω ² = 4.261
                  ω  = [tex]\sqrt{4.261}[/tex]
                  ω  = 2.06 rad/second
Angular velocity ω = [tex]\frac{2\pi }{T}[/tex]
where T is the period ⇒ time taken to complete one revolution
Substituting the calculated value of ω into the equation to solve for period T
                  2.06  = [tex]\frac{2\pi }{T}[/tex]
                  T = [tex]\frac{2\pi }{2.06}[/tex]
                  T = 3.05 seconds
The revolutions per minute = [tex]\frac{60}{3.05}[/tex]
                       = 11.67 revolutions per minute
