A plane is inclined at an angle $\theta$ to the horizontal. Its velocity ratio is

Analyze the question: An inclined plane is a simple machine. We need its velocity ratio (VR) in terms of the angle θ.

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

For an inclined plane:

• The effort is applied along the slope, so it moves a distance equal to the length of the plane, L.
• The load is raised vertically through the height of the plane, h.

Solution:

VR = distance moved by effort / distance moved by load = L / h

From the right-angled triangle formed by the plane:

sin θ = h / L, so L / h = 1 / sin θ

Therefore:

VR = 1 / sin θ

Check: If θ is small (a gentle slope), sin θ is small, so VR is large. This makes sense because a gentle slope lets you lift a heavy load with a small effort, over a long distance.

Answer: C

Tip: For an inclined plane, remember "VR = length ÷ height = 1/sin θ". The ideal mechanical advantage equals the VR when friction is ignored. Also, the efficiency is MA/VR × 100%, which is often tested together with this.