Which of the following statements is correct about a machine?

1. Analyze the question

The question asks us to identify the correct relationship between a machine's efficiency, friction, velocity ratio, and mechanical advantage. To answer this, we must understand the fundamental principles of simple machines.

2. Explain the concept

• Efficiency ($\eta$): This is the ratio of the work output to the work input, usually expressed as a percentage. It is also defined as the ratio of Mechanical Advantage (MA) to Velocity Ratio (VR): $$\eta = \frac{\text{MA}}{\text{VR}} \times 100\%$$
• Friction: In any real-world machine, friction is always present. Friction causes some of the input energy to be dissipated as heat. As friction increases, the work output decreases for the same amount of work input, which directly lowers the efficiency.
• Velocity Ratio (VR): This is determined by the geometry or design of the machine (e.g., the number of pulleys or the length of a lever). It is independent of friction.
• Mechanical Advantage (MA): This is the ratio of the load to the effort. Friction reduces the effective output force, meaning that as friction increases, the MA actually decreases.

3. Show the solution

• Option A: Efficiency is always less than 1 (or 100%) because no machine is perfectly frictionless. Therefore, A is incorrect.
• Option B: Since efficiency is defined by how much input energy is successfully converted to useful output, and friction wastes energy as heat, an increase in friction will always result in a lower efficiency. This statement is correct.
• Option C: Velocity ratio is a mechanical property based on the machine's construction (distance moved by effort / distance moved by load). Friction does not change the geometry of the machine. Therefore, C is incorrect.
• Option D: Mechanical advantage is the ratio of load to effort. Friction opposes motion, requiring more effort to move the same load. This decreases the MA, not increases it. Therefore, D is incorrect.

4. Identify the answer

The correct statement is that efficiency decreases as friction increases.

5. Tip

When dealing with machine questions, remember the "Ideal vs. Real" rule:

• Ideal Machine: Efficiency = 100% (No friction).
• Real Machine: Efficiency < 100% (Friction is present).
• Golden Rule: Friction is the enemy of efficiency! Whenever friction goes up, efficiency must go down.