A simple pendulum has a period T$=2\mathrm{.}24$T$=2\mathrm{.}24$s in a location where g$=9\mathrm{.}80000$g$=9\mathrm{.}80000$m$/$s$2\mathrm{.}2.$ You can assume that the accuracy of the period TT is good to $6$ significant digits. When you work out your solutions for this problem, be sure to keep $6$ significant digits.

$($a$)$

What is its length?

m $(2$E$-5$ m$)$

$($b$)$

What would be its period on the moon where g$=1\mathrm{.}67000$g$=1\mathrm{.}67000$m$/$s$22?$

s $(0\mathrm{.}02$ s$)$

$($c$)$

What is the difference in the period between a location where g$=9\mathrm{.}80000$g$=9\mathrm{.}80000$m$/$s$22$ and a location where g$=9\mathrm{.}79000$g$=9\mathrm{.}79000$m$/$s$22?$

s $(2$E$-5$ s$)$