Answer
a. $0.816ft$
b. $0.00613sec$
c. Lose $530sec\approx8.83min$ in a day
Work Step by Step
a. Given $T^2=4\pi^2L/g$, we have $L=\frac{T^2g}{4\pi^2}=\frac{(1)^2(32.2)}{4\pi^2}\approx0.816ft$
b. Taking the derivative of the above equation, we get $dL=\frac{2Tg}{4\pi^2}dT$. With $dL=0.01ft$, we have $dT=\frac{2\pi^2}{Tg}dL=\frac{2\pi^2}{32.2}(0.01)\approx0.00613sec$
c. In a full day of 24 hours, the clock will swing $n=24\times60\times60=86400$ times. As the new period is longer than before, we will lose time with an amount of $\Delta t=86400\times0.0613\approx530sec\approx8.83min$
