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 $=0\mathrm{.}2484$ m and, instead of keeping perfect time, the clock runs slow by $1\mathrm{.}506$ minutes per day.

HINT

$($a$)$

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

$9\mathrm{.}788$ 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.$)$

$0\mathrm{.}2479$ m