A clock is constructed so that it keeps perfect time when its simple pendulum has a period of $1\mathrm{.}000$ s at locations where

g $=9\mathrm{.}800$ m$/$s$.$ The pendulum bob has length L $=0\mathrm{.}2482$ m$,$

and instead of keeping perfect time, the clock runs slow by $1\mathrm{.}500$ minutes per day. $($a$)$ What is the free$-$fall acceleration at the clock's location? $($b$)$ What length of pendulum bob is required for the clock to keep perfect time?