To determine the efficiency of a wheel and axle system used to raise a load, we need to follow a systematic approach. Let's break down the problem step-by-step. ### Step 1: Understanding the Problem We have: - Load (output force) = 500 N - Effort (input force) = 250 N - Radius of the wheel (R_wheel) = 0.4 cm = 0.004 m (convert to meters for calculations) - Radius of the axle (R_axle) = 0.1 cm = 0.001 m (convert to meters for calculations) ### Step 2: Calculate the Mechanical Advantage (MA) The Mechanical Advantage (MA) of a machine is defined as the ratio of the load force to the effort force. It tells us how much the machine multiplies the input force. \[ \text{MA} = \frac{\text{Load}}{\text{Effort}} = \frac{500 \, \text{N}}{250 \, \text{N}} = 2 \] ### Step 3: Calculate the Velocity Ratio (VR) The Velocity Ratio (VR) for a wheel and axle is given by the ratio of the radius of the wheel to the radius of the axle. This tells us how much distance the effort moves compared to the distance the load moves. \[ \text{VR} = \frac{R_{\text{wheel}}}{R_{\text{axle}}} = \frac{0.004 \, \text{m}}{0.001 \, \text{m}} = 4 \] ### Step 4: Calculate the Efficiency Efficiency (\(\eta\)) of a machine is calculated using the formula: \[ \eta = \frac{\text{MA}}{\text{VR}} \times 100\% \] Substituting the values we calculated: \[ \eta = \frac{2}{4} \times 100\% = 0.5 \times 100\% = 50\% \] ### Conclusion The efficiency of the wheel and axle system is **50%**. Therefore, the correct option is **C**. ### Step 5: Explanation of Other Options - **Option A (20%)**: This option is incorrect because it suggests a much lower efficiency than what we calculated. An efficiency of 20% would imply that the machine is very inefficient, which is not the case here. - **Option B (40%)**: This option is also incorrect. It is lower than our calculated efficiency of 50%. It does not accurately reflect the relationship between the load and effort in this scenario. - **Option D (60%)**: This option is incorrect as well. It suggests a higher efficiency than what we calculated. An efficiency of 60% would imply that the machine is performing better than it actually is based on the given load and effort. ### Common Pitfalls 1. **Unit Conversion**: Always ensure that units are consistent (e.g., converting cm to m) before performing calculations. 2. **Understanding MA and VR**: Confusing the definitions of Mechanical Advantage and Velocity Ratio can lead to incorrect efficiency calculations. 3. **Efficiency Interpretation**: Remember that efficiency is always a percentage and should be between 0% and 100%. ### Revision Summary - **Mechanical Advantage (MA)** is the ratio of load to effort. - **Velocity Ratio (VR)** is the ratio of the radius of the wheel to the radius of the axle. - **Efficiency** is calculated as \(\eta = \frac{\text{MA}}{\text{VR}} \times 100\%\). - The efficiency of the given wheel and axle system is **50%** (Option C).