David cuts a rope 60 m long into two pieces in the ratio 2:3. What is the length of the shorter piece of rope?

1. Let the lengths of the two pieces of rope be represented as $2x$ and $3x$, since they are in the ratio 2:3.

2. According to the problem, the sum of the lengths of the two pieces is 60 m, so:
2x + 3x = 60

3. Combine like terms:
5x = 60

4. Solve for $x$:
x = \frac{60}{5}
x = 12

5. The length of the shorter piece of rope is $2x$, so:
2x = 2 \times 12
2x = 24

6. Therefore, the length of the shorter piece of rope is:
24 \, \text{m}