A grandfather clock should beat seconds, so its pendulum should have a period of 2.00 s…

(a) The right length. We want $L$, so $L = \dfrac{gT^2}{4\pi^2} = \dfrac{9.81\ \text{m/s}^2 \times (2.00\ \text{s})^2}{4\pi^2} = 0.994\ \text{m}$.

(b) The new period. Now $L = 1.004\ \text{m}$:

(c) Time lost. In one day the pendulum makes $\dfrac{86400\ \text{s}}{2.010\ \text{s}} = 42984$ swings. The clock counts $2.00\ \text{s}$ for each, so it shows $85969\ \text{s}$. It loses about $431\ \text{s}$, a little over seven minutes.