The 'seconds' hand on the watch goes all the way around in 1 minute. 15 seconds is 1/4 of a complete 1-minute revolution. So, the 2 cm is 1/4 of the way around the circle that the tip makes. This makes the full circumference of the circle 8cm.
The length of the second hand will be the radius of the circle. Use the following equation:
2 pi radius = circumference
Since we know the circumference, plug that in, and solve for the radius:
2 pi radius = 8 cm
radius = 8cm / 2 pi = 1.27 cm