A grandfather clock is controlled by a swinging brass pendulum that is $1\mathrm{.}4$ m long at a temperature of $28C.$

$($a$)$ What is the length of the pendulum rod when the temperature drops to $0\mathrm{.}0C?($Give your answer to at least four significant figures.$)$

$1\mathrm{.}042e^{-3}$

Your response differs significanty from the correct answer. Rework your solution from the beginning and check each step carefully, mm

$($b$)$ If a pendulum's period is given by $T=2\sqrt[\phantom{2}]{\frac{L}{g}},$ where $L$ is its length, does the change in length of the rod cause the clock to run fast or slow?

fast

slow

neither

Please show me how to solve step by step