Question

In the image shown below, all pulleys are fixed. If the load needs to be lifted by a height of 8 m, by how much distance will the truck have to move? 

• A. 8 m
• B. 6 m
• C. 4 m
• D. 2 m

Hint:

In physics problems, if the text provides a condition that contradicts a diagram (e.g., "all pulleys are fixed" vs. a diagram showing a movable pulley), first check if calculations based on the text lead to one of the given answers. This is often the intended path to the solution.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem involves a pulley system. The key is to understand the relationship between the distance the load is lifted and the distance the effort (the truck) moves. This relationship is determined by the type of pulley system.
Step 2: Key Formula or Approach:
For any pulley system, the distance moved by the effort (`\(d_E\)`) is related to the distance moved by the load (`\(d_L\)`) by the Velocity Ratio (VR) of the system:
\[ d_E = \text{VR} \times d_L \] The Velocity Ratio depends on the pulley arrangement. For a system composed \textit{only} of fixed pulleys, the VR is 1. Fixed pulleys only change the direction of the force and do not provide any mechanical advantage.
Step 3: Detailed Explanation:
There is a contradiction between the question's text and its accompanying diagram.
- The Diagram: The diagram shows a system with two fixed pulleys at the top and one \textit{movable} pulley attached to the load. In such a system, there are two segments of the rope supporting the load, which would give a Velocity Ratio of 2. If we were to follow the diagram, the truck would have to move \(2 \times 8 \, \text{m} = 16 \, \text{m}\), which is not an option.
- The Text: The question explicitly states, "all pulleys are fixed." In competitive exams, when there is a conflict between the text and a diagram, the text often takes precedence, especially if calculations based on the text lead to a valid option.
Following the statement that all pulleys are fixed, the system's Velocity Ratio (VR) is 1.
Using the formula:
\[ d_E = \text{VR} \times d_L \] \[ d_E = 1 \times 8 \, \text{m} \] \[ d_E = 8 \, \text{m} \] Therefore, to lift the load by 8 m, the truck must move 8 m.
Step 4: Final Answer:
Assuming the text "all pulleys are fixed" is the intended condition for the problem, the truck must move a distance of 8 m.