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
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
