Final answer:
If the Earth's rate of rotation were to increase, the day would be shorter because a faster rotation would mean less time for one complete turn on its axis, with no effect on the length of the year.
Step-by-step explanation:
If the Earth's rate of rotation were to increase, the day would be shorter. This is because the length of a day is determined by the time it takes for the Earth to complete one full rotation on its axis.
An increase in the rotation speed means that this rotation would take less time to complete, thereby shortening the length of the day. The year is based on the Earth's orbit around the Sun, not its rotation, so the length of the year would remain unaffected. Therefore, the correct answer is: 2) The day would be shorter.