Given:
- Load \( W = 180 \, \text{N} \)
- Efficiency \( \eta = 90\% = 0.9 \)
- Let the effort \( E \) be applied.

The efficiency of a machine is given by the formula:

\(\eta = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}}\)

Mechanical Advantage (MA) is defined as the ratio of load to effort:

\(\text{MA} = \frac{W}{E}\)

 Determine the Velocity Ratio (VR)

Given that the effort arm is twice the load arm, we can express the Velocity Ratio (VR) as:

\(\text{VR} = \frac{\text{Length of effort arm}}{\text{Length of load arm}} = \frac{2L}{L} = 2\)

 Substitute into the efficiency formula

Substituting the expressions for MA and VR into the efficiency formula gives:

\(0.9 = \frac{\frac{W}{E}}{2}\)

Rearrange to find the effort \( E \)

Multiplying both sides by \( 2E \):

\(1.8E = W\)

Substituting \( W = 180 \, \text{N} \):

\(
1.8E = 180\)

Solve for \( E \)

Now, dividing by 1.8:

\(E = \frac{180}{1.8} = 100 \, \text{N}\)

Therefore, the effort applied by the machine is: \(\boxed{100 \, \text{N}}\).