The efficiency of a wheel and axle is 100% and the ratio of their radii is 5:1. calculate the effort required…

Analyze the question

We have a wheel and axle with 100% efficiency. The ratio of the radii (wheel : axle) is 5:1, and we must find the effort needed to lift a 20 kg load.

Concept

For a wheel and axle:

• Velocity ratio (VR) = radius of wheel / radius of axle = R/r
• Mechanical advantage (MA) = Load / Effort
• Efficiency = (MA / VR) × 100%

Solution

1. Load = mg = 20 × 10 = 200 N
2. VR = 5/1 = 5
3. Efficiency = 100%, so MA = VR = 5
4. Effort = Load / MA = 200 / 5 = 40 N

Check: Taking moments about the axis, Effort × R = Load × r, so Effort = 200 × (1/5) = 40 N. ✔

Answer: 40 N, which is option C.

Tip: With 100% efficiency (an ideal machine), MA = VR. Always convert mass to weight first (W = mg), because load and effort are forces measured in newtons, not kilograms. A common trap is using 20 instead of 200 and getting 4 N, or dividing wrongly and getting 100 N.