The velocity ratio of an inclined plane

Analyze the question: We need to know how the velocity ratio (VR) of an inclined plane changes with the angle of inclination θ.

Concept: Velocity ratio = distance moved by the effort ÷ distance moved by the load.

For an inclined plane:

• The effort moves along the slope, a distance L (the length of the incline).
• The load is raised vertically through a height h.

So:

VR = L / h = 1 / sin θ

(because sin θ = h / L)

Step-by-step analysis:

• If θ increases, sin θ increases, so VR = 1/sin θ decreases.
• If θ decreases, sin θ decreases, so VR = 1/sin θ increases.

Check with numbers:

• θ = 30°: VR = 1/0.5 = 2
• θ = 60°: VR = 1/0.866 ≈ 1.15
• θ = 10°: VR = 1/0.174 ≈ 5.76

As the angle gets smaller, the VR gets larger. This matches the idea that a gentler slope makes the effort travel a longer distance for the same height gained.

Evaluating the options:

• A. Wrong, since VR decreases as θ increases.
• B. Correct, since VR increases as θ decreases.
• C. Wrong, since it is the opposite of the true relationship.
• D. Wrong, since VR clearly depends on θ.

Tip: Remember VR = 1/sin θ. A gentle slope (small angle) means a large VR, which is why long ramps make loading heavy items easier. Small angle → big VR → less effort needed (though more distance travelled).