# Efficiency Calculation for a Machine Given: - **Velocity Ratio (V.R.)** = \( \frac{1}{8} \) - **Mechanical Advantage (M.A.)** = \( \frac{1}{3} \) We are to find the **efficiency** of the machine. --- ## Step 1: Write the Efficiency Formula Efficiency (\( \eta \)) of a machine is given by: \[ \text{Efficiency} = \frac{\text{Mechanical Advantage}}{\text{Velocity Ratio}} \] --- ## Step 2: Substitute the Given Values Plug the values into the formula: \[ \text{Efficiency} = \frac{\frac{1}{3}}{\frac{1}{8}} \] --- ## Step 3: Simplify the Fraction Dividing two fractions: \[ \frac{\frac{1}{3}}{\frac{1}{8}} = \frac{1}{3} \times \frac{8}{1} = \frac{8}{3} \] --- ## Step 4: Convert to Percentage Efficiency is generally expressed as a percentage. \[ \frac{8}{3} \times 100\% = 266.67\% \] --- ## Step 5: Interpretation - An efficiency greater than 100% is **not physically possible** for a real machine. This suggests the velocity ratio and mechanical advantage values might have been interchanged or misinterpreted. - Usually, **velocity ratio** is a **number greater than 1** and **mechanical advantage** is usually less than velocity ratio. --- ## Final Answer **Calculated Efficiency:** \[ \boxed{266.67\%} \] > **Note:** This result is not physically possible for a real machine. Please double-check the given values for velocity ratio and mechanical advantage; the correct efficiency should always be less than or equal to 100%.