Lifting Machines – Mechanical Advantage vs Velocity Ratio For actual (real) machines with frictional losses, the mechanical advantage (MA) is __________ the velocity ratio (VR).

Introduction / Context:
In machine theory, the velocity ratio (VR) is a geometric/kinematic property, while the mechanical advantage (MA) depends on actual forces and is reduced by friction. Efficiency bridges the two.

Given Data / Assumptions:

• Efficiency η = MA / VR.
• For real machines, 0 < η < 1 due to losses.

Concept / Approach:
Rearranging efficiency gives MA = η * VR. Since η < 1 in real machines, MA < VR.

Step-by-Step Solution:
Start: η = MA / VR. Rearrange: MA = η * VR. With η < 1 ⇒ MA < VR.

Verification / Alternative check:
Ideal machine has η = 1 ⇒ MA = VR; adding friction reduces MA below VR.

Why Other Options Are Wrong:
Equal to: only for ideal machines. Greater than or reciprocal: contradicts η < 1. Unrelated: incorrect; η links them directly.

Common Pitfalls:
Confusing MA with VR or ignoring efficiency.

Final Answer:
less than