Question

In actual machines ____________.

• A. mechanical advantage is greater than velocity ratio
• B. mechanical advantage is equal to velocity ratio
• C. mechanical advantage is less than velocity ratio
• D. mechanical advantage is unity

Hint:

To quickly solve this:
Recall that friction always reduces output force.
Since \(\text{Mechanical Advantage} = \text{Efficiency} \times \text{Velocity Ratio}\), and efficiency in real life is always less than 1, Mechanical Advantage must be less than Velocity Ratio.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A machine is a device that simplifies work by multiplying force or changing its direction.
The performance of a machine is characterized by:
- Mechanical Advantage (MA): The ratio of the output force (load, \(W\)) to the input force (effort, \(P\)):
\[ \text{MA} = \frac{W}{P} \]
- Velocity Ratio (VR): The ratio of the distance moved by the effort (\(d_P\)) to the distance moved by the load (\(d_W\)):
\[ \text{VR} = \frac{d_P}{d_W} \]
- Efficiency (\(\eta\)): The ratio of work output to work input.
Key Formula or Approach:
The relationship between efficiency, mechanical advantage, and velocity ratio is:
\[ \text{Efficiency } (\eta) = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \]

Step 2: Detailed Explanation:
Let us analyze the differences between ideal and actual machines:
- In an ideal machine, there are no losses due to friction, air resistance, or elastic deformation.
Therefore, the efficiency is 100% (\(\eta = 1.0\)), which means:
\[ \text{MA} = \text{VR} \]
- In an actual machine, some energy is always lost overcoming friction between moving parts, sliding resistance, and other physical losses.
Therefore, the efficiency is always less than 100% (\(\eta < 1.0\)).
Using the formula:
\[ \eta = \frac{\text{MA}}{\text{VR}} < 1.0 \implies \text{MA} < \text{VR} \]
Thus, in all actual machines, the mechanical advantage is always less than the velocity ratio.
This matches Option (C).

Step 3: Final Answer:
The correct option is (C).