The pendulum of a large clock consists of a thin steel rod with a heavy weight at the end. At 20 degrees C the rod is 1.22 meters long and the clock keeps accurate time. (a) By how much does the length of the steel rod change if the temperature rises to 40 degrees C? (b) Does the clock run fast or slow-explain why. (c) What is the fractional change in the period of the pendulum (hint: treat the change in length as an error and use propagation of error). (d) By how many seconds per day does the clock gain or lose time?