Sure, let's solve the problem step-by-step.
1. First, understand and note the given data:
- The actual mechanical advantage (AMA) of the pulley is 2.
- There are 3 supporting strings, which gives the ideal mechanical advantage (IMA) as 3.
2. Recall the formula to calculate the efficiency of a pulley:
[tex]\[
\text{Efficiency} = \left(\frac{\text{Actual Mechanical Advantage (AMA)}}{\text{Ideal Mechanical Advantage (IMA)}}\right) \times 100
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Efficiency} = \left(\frac{2}{3}\right) \times 100
\][/tex]
4. Perform the division and multiplication to find the efficiency:
[tex]\[
\frac{2}{3} \approx 0.6666666666666666
\][/tex]
[tex]\[
0.6666666666666666 \times 100 = 66.66666666666666
\][/tex]
5. Therefore, the efficiency of the pulley is:
[tex]\[
66 \%
\][/tex]
So, the correct answer from the given options is:
[tex]\[
\boxed{66\%}
\][/tex]
