The diagrams below show four pulley systems. State which of the statements following the diagrams is true.

1. There are three pulley systems with V.R. = 2 and one pulley system with V.R. = 1.
2. There are two pulley systems with V.R. = 2, one pulley system with V.R. = 3 and one pulley system with V.R. = 1.
3. There are two pulley systems with V.R. = 2, one pulley system with V.R.= 3 and one pulley system with V.R. = 4.
4. There are two pulley systems with V.R. = 2 and two pulley system with V.R. = 3.

There are two pulley systems with V.R. = 2 and two pulley system with V.R. = 3

Reason — The velocity ratio is always equal to the number of strands of the tackle (or number of sections of the strings)

Velocity Ratio (V.R.) = $\dfrac{\text{displacement of effort}}{\text{displacement of load}}$

In Figure 1:

Number of sections of the strings = 3

So, the effort must move 3 units of distance to raise the load by 1 unit.

Velocity ratio = $\dfrac{\text{displacement of effort}}{\text{displacement of load}}$

Velocity ratio = $\dfrac{3\text{d}}{\text{d}}=3$

In Figure 2:

Number of sections of the strings = 2

So, the effort must move 2 units of distance to raise the load by 1 unit.

Velocity ratio = $\dfrac{\text{displacement of effort}}{\text{displacement of load}}$

velocity ratio = $\dfrac{2\text{d}}{\text{d}}=2$

In Figure 3:

Number of sections of the strings = 3,

So, the effort must move 3 units of distance to raise the load by 1 unit.

Velocity ratio = $\dfrac{\text{displacement of effort}}{\text{displacement of load}}$

Velocity ratio $= \dfrac{3\text{d}}{\text{d}}=3$

In Figure 4:

Number of sections of the strings = 2,

So, the effort must move 2 units of distance to raise the load by 1 unit.

Velocity ratio = $\dfrac{\text{displacement of effort}}{\text{displacement of load}}$

Velocity ratio = $\dfrac{2\text{d}}{\text{d}}=2$