Answer:
T=56.77s
Explanation:
We must use the formula for centripetal acceleration:
[tex]a_{cp}=\frac{v^2}{r}[/tex]
We know the radius r and we want is to obtain a centripetal acceleration equal to g. Since velocity is distance over time, on this circle we can take distance as the circumference (which is of value [tex]2\pi r[/tex]) and thus the time will be the period T because that's the time a point takes to travel the whole circumference, so we can write:
[tex]g=a_{cp}=\frac{v^2}{r}=\frac{(\frac{2\pi r}{T})^2}{r}[/tex]
or:
[tex]g=\frac{4\pi^2 r}{T^2}[/tex]
and since we want the period:
[tex]T=\sqrt{\frac{4\pi^2 r}{g}}=2\pi\sqrt{\frac{r}{g}}[/tex]
which for our values is:
[tex]T=2\pi\sqrt{\frac{(800m)}{(9.8m/s^2)}}=56.77s[/tex]
