A $52\mathrm{.}1$ cm$-$long pendulum takes $2\mathrm{.}50$ minutes to undergo $101\mathrm{.}9$ complete back$-$and$-$forth cycles.

$($a$)$

Compute the pendulum's period $($in s$).$

s

$($b$)$

Determine the acceleration due to gravity $($in m$/$s$2)$ at the place where the pendulum is located.

m$/$s$2$