Submission $2(10/20$ points$)$ Monday, December $2,202409$:$36$ AM CST

A clock is constructed so that it keeps perfect time when its simple pendulum has a period of exactly $1\mathrm{.}000$ s $.$ The pendulum bob has length $L=0\mathrm{.}2488m$ and, instead of keeping perfect time, the clock runs slow by $1\mathrm{.}505$ minutes per day.

$($a$)$ What is the free$-$fall acceleration $($in $\frac{m}{s^2})$ at the clock's location? $($Give your answer to at least $3$ decimal places.$)$

$\frac{m}{s^2}$

$($b$)$ What length of pendulum bob $($in m $)$ is required for the clock to keep perfect time? $($Give your answer to at least $4$ decimal places.$)$