If the velocity ratio of a machine is 4, what does it mean?

1. Analyze the question

The question asks for the physical interpretation of a Velocity Ratio (V.R.) of 4 in a simple machine.

2. Explain the concept

In Physics, the Velocity Ratio (V.R.) of a machine is defined as the ratio of the distance moved by the effort ($d_e$) to the distance moved by the load ($d_l$) in the same time interval.

The formula is:

When a machine has a V.R. of 4, it means that for every unit of distance the load moves, the effort must move 4 times that distance. This is a fundamental principle of machines: what you lose in distance (by moving the effort further), you gain in force (mechanical advantage).

3. Show the solution

• Given: $V.R. = 4$
• Using the formula: $4 = \frac{d_e}{d_l}$
• Rearranging the equation: $d_e = 4 \times d_l$

This confirms that the distance moved by the effort ($d_e$) is 4 times the distance moved by the load ($d_l$).

• Option A is incorrect because if the load and effort were equal, the Mechanical Advantage would be 1, not necessarily related to the V.R.
• Option C is incorrect because V.R. does not determine efficiency; efficiency depends on the relationship between Mechanical Advantage and V.R.
• Option D is incorrect because the load being greater than the effort refers to the Mechanical Advantage, not the Velocity Ratio.

4. Identify the answer

The correct interpretation is that the effort travels four times the distance that the load travels. This matches Option B.

5. Tip

Remember the mnemonic "V.E.L.": Velocity ratio = Effort distance / Load distance. Always keep in mind that V.R. is purely a measure of distance, while Mechanical Advantage (M.A.) is a measure of force.