Velocity ratio (VR) of a lifting machine: A load of 500 kg is lifted through 13 cm while the effort of 25 kg moves through 650 cm. Based on the definition VR = distance moved by effort / distance moved by load, determine the velocity ratio of the machine.

Introduction / Context:
Velocity ratio (VR) is a fundamental performance parameter of simple machines such as winches, pulleys, and screw jacks. It relates how far the effort moves compared to how far the load is lifted, independent of losses. Understanding VR helps estimate mechanical advantage and efficiency for practical lifting systems.

Given Data / Assumptions:

• Load movement (rise) = 13 cm.
• Effort movement (pull) = 650 cm.
• VR is defined using distances only, not forces.
• No need to convert cm to m since it is a ratio of like units.

Concept / Approach:
For any ideal machine, VR = distance moved by effort / distance moved by load. This geometric ratio reflects the kinematics of the mechanism (e.g., number of rope segments supporting the load, screw lead vs. circumference, etc.).

Step-by-Step Solution:

Verification / Alternative check:
Dividing both distances by 13 confirms that the effort travels 50 times farther than the load, consistent with a high-advantage mechanism (at the cost of larger effort travel).

Why Other Options Are Wrong:

• 55, 60, 65, 70: these arise only if one misreads distances or mixes units. The exact integer division 650/13 equals 50.

Common Pitfalls:
Confusing VR with mechanical advantage (MA). VR uses distances; MA uses forces (load/effort). Efficiency is MA/VR.

Final Answer:
50