Question

The Velocity Ratio (VR) of a block and tackle system of two pulleys with the effort in the upward direction is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

For any block and tackle pulley system, the Velocity Ratio (VR) is simply equal to the total number of pulleys used in the system.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the Velocity Ratio (VR) of a block and tackle system that has a total of two pulleys.
Step 2: Key Formula or Approach:
In an ideal block and tackle system, the Velocity Ratio (VR) is defined as the ratio of the distance moved by the effort (\(d_E\)) to the distance moved by the load (\(d_L\)).
\[ VR = \frac{d_E}{d_L} \] For a block and tackle system, the VR is equal to the total number of pulleys in the system, which is also equal to the number of rope segments supporting the load.
\[ VR = n \] where \(n\) is the total number of pulleys.
Step 3: Detailed Explanation:
The problem states that the block and tackle system has a total of two pulleys (\(n=2\)).
In a typical setup with two pulleys, there would be one fixed pulley in the upper block and one movable pulley in the lower block. The load is supported by two segments of the rope.
When the effort end of the rope is pulled by a distance \(d_E\), each of the two supporting rope segments shortens by \(d_L\). Therefore, the load moves up by a distance \(d_L\), and \(d_E = 2 \times d_L\).
Using the formula for VR:
\[ VR = \frac{d_E}{d_L} = \frac{2 \times d_L}{d_L} = 2 \] Alternatively, using the direct relationship for a block and tackle system:
\[ VR = \text{total number of pulleys} = 2 \] The phrase "effort in the upward direction" describes a specific arrangement, but in a standard block and tackle, the VR depends only on the number of pulleys.
Step 4: Final Answer:
Given that there are two pulleys in the system, the Velocity Ratio is 2.